Physics · Textbook solutions

Ray Optics and Optical Instruments

Every solved example, exercise, and miscellaneous question, in the order the textbook teaches them. Plus every board question asked from this chapter. · 47 questions

Worked Examples

8 q

Solved Examples

Worked · 8

Eg 9.1 $Suppose that the lower half of the concave mirror's reflecting surface in Fig. 9.6 is covered with an opaque (non-reflective) material. What effect will this have on the image of an object placed in front of the mirror?$
Eg 9.2 $A mobile phone lies along the principal axis of a concave mirror, as shown in Fig. 9.7. Show by suitable diagram, the formation of its image. Explain why the magnification is not uniform. Will the distortion of image depend on the location of the phone with respect to the mirror?$
Eg 9.3 $10\,\text{cm}$
Eg 9.4 $R = 2\,\text{m}$
Eg 9.5 $n = 1.5$
Eg 9.6 $n = 1.47$
Eg 9.7 $f = 0.5\,\text{m}$
Eg 9.8 $Find the position of the image formed by the lens combination given in the Fig. 9.20.$

Exercises

39 q

Ex 9.1 $2.5\,\text{cm}$
Ex 9.2 $4.5\,\text{cm}$
Ex 9.3 $12.5\,\text{cm}$
Ex 9.4 $60^\circ$
Ex 9.5 $80\,\text{cm}$
Ex 9.6 $40^\circ$
Ex 9.7 $1.55$
Ex 9.8 $12\,\text{cm}$
Ex 9.9 $3.0\,\text{cm}$
Ex 9.10 $30\,\text{cm}$
Ex 9.11 $2.0\,\text{cm}$
Ex 9.12 $25\,\text{cm}$
Ex 9.13 $144\,\text{cm}$
Ex 9.14 $15\,\text{m}$
Ex 9.15(a) $f$
Ex 9.15(b) $Use the mirror equation to deduce that: (b) a convex mirror always produces a virtual image independent of the location of the object. [Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]$
Ex 9.15(c) $Use the mirror equation to deduce that: (c) the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole. [Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]$
Ex 9.15(d) $Use the mirror equation to deduce that: (d) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image. [Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]$
Ex 9.16 $50\,\text{cm}$
Ex 9.17 $1.68$
Ex 9.18 $3\,\text{m}$
Ex 9.19 $90\,\text{cm}$
Ex 9.20 $8.0\,\text{cm}$
Ex 9.21 $60^\circ$
Ex 9.22 $1\,\text{mm}^{2}$
From Exercise 9.22: a card sheet divided into squares each of size $1\,\text{mm}^{2}$ is viewed through a magnifying glass (a converging lens of focal length $9\,\text{cm}$ ) held close to the eye.
Ex 9.23 $(a) At what distance should the lens be held from the card sheet in Exercise 9.22 in order to view the squares distinctly with the maximum possible magnifying power? (b) What is the magnification in this case? (c) Is the magnification equal to the magnifying power in this case? Explain.$
From Exercise 9.22: a card sheet divided into squares each of size $1\,\text{mm}^{2}$ is viewed through a magnifying glass (a converging lens of focal length $9\,\text{cm}$ ) held close to the eye.
Ex 9.24 $6.25\,\text{mm}^{2}$
Ex 9.25(a) $Answer the following questions: (a) The angle subtended at the eye by an object is equal to the angle subtended at the eye by the virtual image produced by a magnifying glass. In what sense then does a magnifying glass provide angular magnification?$
Ex 9.25(b) $Answer the following questions: (b) In viewing through a magnifying glass, one usually positions one's eyes very close to the lens. Does angular magnification change if the eye is moved back?$
Ex 9.25(c) $Answer the following questions: (c) Magnifying power of a simple microscope is inversely proportional to the focal length of the lens. What then stops us from using a convex lens of smaller and smaller focal length and achieving greater and greater magnifying power?$
Ex 9.25(d) $Answer the following questions: (d) Why must both the objective and the eyepiece of a compound microscope have short focal lengths?$
Ex 9.25(e) $Answer the following questions: (e) When viewing through a compound microscope, our eyes should be positioned not on the eyepiece but a short distance away from it for best viewing. Why? How much should be that short distance between the eye and eyepiece?$
Ex 9.26 $30\text{X}$
Ex 9.27(a) $140\,\text{cm}$
Ex 9.27(b) $140\,\text{cm}$
Ex 9.28 $100\,\text{m}$
Ex 9.29 $20\,\text{mm}$
Ex 9.30 $3.5^\circ$
Ex 9.31 $1.50$

What the board has asked from this chapter

Questions per paper · 26 papers · 2022 to 2026

Bars average the full papers of each year. 54 further questions come from set variants and are listed below.

2026

45 q

3 $An equiconvex lens of focal length 15 cm is cut into two equal plano-convex halves. The focal length of each half will be :$
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Refraction at Spherical Surfaces and by Lenses
4 $\mu$
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Refraction at Spherical Surfaces and by Lenses
5 $1{\cdot}5$
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Refraction at Spherical Surfaces and by Lenses
5 $A concave lens of focal length 40 cm is coaxially in contact with two convex lenses, each of focal length 20 cm, on each side. The focal length of the combination is$
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Refraction at Spherical Surfaces and by Lenses
6 $6{\cdot}0$
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Optical Instruments
7 $In which of the following, total internal reflection does not occur ?$
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Refraction and Total Internal Reflection
7 $Light from a small object in air falls on a spherical glass surface (n = 1.5) of radius of curvature R. A real image of the object will be formed if the object distance u is related to R as :$
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Refraction at Spherical Surfaces and by Lenses
9 $A concave lens of focal length 10 cm is cut into two identical plano-concave lenses. The focal length of each lens will be$
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Refraction at Spherical Surfaces and by Lenses
9 $A ray of yellow light undergoes total internal reflection when it is incident at the interface of two media. This ray is successively replaced by the ray of blue, green and red lights. Which of the following statements is true if the angle of incidence is same in all cases ?$
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Refraction and Total Internal Reflection
Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
15 $Assertion (A) : When a convex lens made of glass is immersed in water, its converging power increases. Reason (R) : The focal length of a lens depends only on the radii of curvature of its two faces.$
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Refraction at Spherical Surfaces and by Lenses
18 $\sqrt{2}$
Refraction and Total Internal Reflection
19 $\angle i$
Refraction Through a Prism
19 $A concave mirror of radius of curvature 16 cm produces two-times enlarged real image of an object kept in front of it. Find the position of the object.$
Reflection by Spherical Mirrors
19 $12{\cdot}5$
Refraction and Total Internal Reflection
19 $\sqrt{2}$
Refraction and Total Internal Reflection
19 $^\circ$
Refraction Through a Prism
20 $Draw a labelled ray diagram of an astronomical telescope when final image is formed at infinity. Write the expression for its magnifying power.$
Optical Instruments
21 (a) $A 5 cm long pencil is placed along the principal axis of a concave mirror of focal length 20 cm such that its nearest end is at a distance of 25 cm from the mirror. Calculate the length of the image of the pencil.$
Reflection by Spherical Mirrors
20 $f_1$
Refraction at Spherical Surfaces and by Lenses
20 $1{\cdot}5$
Refraction at Spherical Surfaces and by Lenses
21 $A ray of light is incident at an angle 2A on one of the faces of a glass prism of refracting angle A. After refraction from this face, the ray strikes the opposite face which is silvered. The reflected ray from this face retraces on its path. Trace the ray diagram and find the relation between the refractive index of material of prism and the angle of prism.$
Refraction Through a Prism
21 $1{\cdot}5$
Refraction at Spherical Surfaces and by Lenses
23 $\mu$
Refraction and Total Internal Reflection
23 $45^\circ$
Refraction Through a Prism
26 $\dfrac{3}{2}$
Refraction and Total Internal Reflection
27 $(a) Draw the ray diagram to show the image formation by a refracting telescope and write the expression for angular magnification for the telescope in normal adjustment. (b) Give two reasons to explain why a reflecting telescope is preferred over a refracting telescope.$
Optical Instruments
28 $\frac{3}{4} n$
Refraction and Total Internal Reflection
28 $Draw a labelled ray diagram showing the formation of image by a compound microscope when final image is formed at least distance of distinct vision. Derive an expression for its magnifying power for this case.$
Optical Instruments
28 $L_1$
Optical Instruments
An astronomical telescope consists of two converging lenses. One of them of large aperture and large focal length is called objective lens and the other one, of smaller focal length and smaller aperture is called the eyepiece. It is used to see distant objects which are not seen clearly with naked eyes. The image formed by the objective lens acts as an object for the eyepiece and the final image produced by the eyepiece is magnified.
30 (i) $The images formed by the objective lens and the eyepiece are respectively :$
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Optical Instruments
In an experiment with convex lens of focal length f, the screen is fixed at a distance D from the object. A student slowly moves the lens away from the object towards the screen and finds that she is able to form sharp image of the object for two positions of the lens. The distance between these two positions of the lens is d.
30 (i) $The value of d is$
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Refraction at Spherical Surfaces and by Lenses
In an experiment with convex lens of focal length f, the screen is fixed at a distance D from the object. A student slowly moves the lens away from the object towards the screen and finds that she is able to form sharp image of the object for two positions of the lens. The distance between these two positions of the lens is d.
30 (ii) $Compared to the size of the object, the images formed in the two positions of the lens are respectively$
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Refraction at Spherical Surfaces and by Lenses
An astronomical telescope consists of two converging lenses. One of them of large aperture and large focal length is called objective lens and the other one, of smaller focal length and smaller aperture is called the eyepiece. It is used to see distant objects which are not seen clearly with naked eyes. The image formed by the objective lens acts as an object for the eyepiece and the final image produced by the eyepiece is magnified.
30 (ii) $The magnification produced by the telescope does not depend upon the :$
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Optical Instruments
An astronomical telescope consists of two converging lenses. One of them of large aperture and large focal length is called objective lens and the other one, of smaller focal length and smaller aperture is called the eyepiece. It is used to see distant objects which are not seen clearly with naked eyes. The image formed by the objective lens acts as an object for the eyepiece and the final image produced by the eyepiece is magnified.
30 (iii) $Which of the following statements is not correct for this telescope ?$
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Optical Instruments
In an experiment with convex lens of focal length f, the screen is fixed at a distance D from the object. A student slowly moves the lens away from the object towards the screen and finds that she is able to form sharp image of the object for two positions of the lens. The distance between these two positions of the lens is d.
30 (iii) $If the distance between object and screen is 80.00 cm and the lens forms sharp images at two positions separated by 20.00 cm., the focal length of convex lens is$
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Refraction at Spherical Surfaces and by Lenses
An astronomical telescope consists of two converging lenses. One of them of large aperture and large focal length is called objective lens and the other one, of smaller focal length and smaller aperture is called the eyepiece. It is used to see distant objects which are not seen clearly with naked eyes. The image formed by the objective lens acts as an object for the eyepiece and the final image produced by the eyepiece is magnified.
30 (iv) (a) $An astronomical telescope has objective lens and eyepiece of focal lengths 80 cm and 4 cm respectively. To view the image in normal adjustment, the lenses must be separated by a distance of :$
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Optical Instruments
In an experiment with convex lens of focal length f, the screen is fixed at a distance D from the object. A student slowly moves the lens away from the object towards the screen and finds that she is able to form sharp image of the object for two positions of the lens. The distance between these two positions of the lens is d.
30 (iv) (a) $Consider a convex lens of focal length 15 cms. For which of the following values of object-screen distance, two positions of the object can be found to obtain sharp image on the screen ?$
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Refraction at Spherical Surfaces and by Lenses
An astronomical telescope consists of two converging lenses. One of them of large aperture and large focal length is called objective lens and the other one, of smaller focal length and smaller aperture is called the eyepiece. It is used to see distant objects which are not seen clearly with naked eyes. The image formed by the objective lens acts as an object for the eyepiece and the final image produced by the eyepiece is magnified.
30 (iv) (b) $Consider the telescope described in question (iv) (a). Its magnifying power in normal adjustment will be :$
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Optical Instruments
In an experiment with convex lens of focal length f, the screen is fixed at a distance D from the object. A student slowly moves the lens away from the object towards the screen and finds that she is able to form sharp image of the object for two positions of the lens. The distance between these two positions of the lens is d.
30 (iv) (b) $\frac{10}{3}$
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Refraction at Spherical Surfaces and by Lenses
31 (a) $(\mu)$
Refraction Through a Prism
31 (b) $(a) Draw a labelled ray diagram of a refracting telescope when it forms image of a distant object at infinity. Derive expression for its magnifying power. (b) (i) In a telescope the objective has much larger aperture than the eye piece. Why ? (ii) Write two advantages of reflecting telescope over refracting telescope.$
Optical Instruments
32 (a) $L_1$
Refraction at Spherical Surfaces and by Lenses
32 (b) $(a) Draw a ray diagram to show the image formation by a concave mirror when the object is kept between its focus and the centre of curvature. Using this diagram, derive the mirror formula. (b) A concave mirror produces a two times magnified virtual image of an object kept 10 cm in front of it. Calculate the focal length of the mirror.$
Reflection by Spherical Mirrors
33 (a) $(i) A point object is kept in front of a convex spherical surface of radius of curvature R. Draw the ray diagram to show the formation of image and derive the relation between the object and image distance (u and v) in terms of refractive index n of the medium and R. (ii) A convex lens of focal length of 20 cm is used to form the image of an object placed 30 cm away from the lens. Find the position and nature of the image formed.$
Refraction at Spherical Surfaces and by Lenses
33 (b) $(i) With the help of a ray diagram, describe the construction and working of a compound microscope. (ii) (I) The real image of an object placed between f and 2f from a convex lens can be seen on a screen placed at the image location. If the screen is removed, is the image still there ? Explain. (II) Plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances ? Explain.$
Optical Instruments

Lens	$L_1$	$L_2$	$L_3$
Power	6 D	3 D	10 D
Aperture	1 cm	8 cm	1 cm

2025

50 q

8 $n$
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Refraction and Total Internal Reflection
8 $-2{\cdot}0$
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Reflection by Spherical Mirrors
8 $\frac{4}{3}$
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Refraction and Total Internal Reflection
8 $v_1$
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Refraction and Total Internal Reflection
9 $The plane face of a planoconvex lens is silvered. The refractive index of material and radius of curvature of the curved surface of the lens are n and R respectively. This lens will behave as a concave mirror of focal length$
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Refraction at Spherical Surfaces and by Lenses
9 $\frac{5}{3}$
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Reflection by Spherical Mirrors
9 $A tub is filled with a transparent liquid to a height of 30.0 cm. The apparent depth of a coin lying at the bottom of the tub is found to be 16.0 cm. The speed of light in the liquid will be$
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Refraction and Total Internal Reflection
10 $f_o$
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Optical Instruments
10 $\mu = 1{\cdot}5$
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Refraction and Total Internal Reflection
Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
13 $Assertion (A) : In a reflecting telescope, the image does not have chromatic aberration. Reason (R) : Chromatic aberration occurs only due to refraction of light through an optical medium.$
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Optical Instruments
Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
14 $Assertion (A) : A ray of light is incident normally on the face of a prism. The emergent ray will graze along the opposite face of the prism when the critical angle at glass-air interface is equal to the angle of the prism. Reason (R) : The refractive index of a prism depends on angle of the prism.$
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Refraction Through a Prism
18 (a) $Using the mirror equation and the formula of magnification, deduce that "the virtual image produced by a convex mirror is always diminished in size and is located between the pole and the focus."$
Reflection by Spherical Mirrors
18 (a) $A point object is placed in air at a distance R/3 in front of a convex surface of radius of curvature R, separating air from a medium of refractive index n (< 4). Find the nature and position of the image formed.$
Refraction at Spherical Surfaces and by Lenses
18 (b) $1{\cdot}5$
Refraction at Spherical Surfaces and by Lenses
19 $Two convex lenses A and B, each of focal length 10.0 cm, are mounted on an optical bench at 50.0 cm and 70.0 cm respectively. An object is mounted at 20.0 cm. Find the nature and position of the final image formed by the combination.$
Refraction at Spherical Surfaces and by Lenses
19 $1{\cdot}5$
Refraction at Spherical Surfaces and by Lenses
19 $The two surfaces of a biconvex lens are of radius of curvature 'R' each. Obtain the condition under which its focal length 'f' be equal to 'R'. If one of the two surfaces of this lens is made plane, what will be the new focal length of the lens ?$
Refraction at Spherical Surfaces and by Lenses
18 (b) $A convex lens of focal length 10 cm, a concave lens of focal length 15 cm and a third lens of unknown focal length are placed coaxially in contact. If the focal length of the combination is +12 cm, find the nature and focal length of the third lens, if all lenses are thin. Will the answer change if the lenses were thick ?$
Refraction at Spherical Surfaces and by Lenses
19 $A light beam converges at a point O. In the path of this beam, a concave lens of focal length 15 cm is placed at a distance of 10 cm before point O. The beam now converges at a point O'. Find the magnitude and the direction of shift OO'.$
Refraction at Spherical Surfaces and by Lenses
19 $\frac{2}{\sqrt{3}}$
Refraction and Total Internal Reflection
20 $\delta$
Refraction Through a Prism
19 $1{\cdot}55$
Refraction at Spherical Surfaces and by Lenses
19 $Two concave lenses A and B, each of focal length 8.0 cm are arranged coaxially 16 cm apart as shown in figure. An object P is placed at a distance of 4.0 cm from A. Find the position and nature of the final image formed.$
Refraction at Spherical Surfaces and by Lenses
19 $A double convex lens of glass has both faces of the same radius of curvature 17 cm. Find its focal length if it is immersed in water. The refractive indices of glass and water are 1.5 and 1.33 respectively.$
Refraction at Spherical Surfaces and by Lenses
19 $A spherical convex surface of radius of curvature R separates glass (refractive index 1.5) from air. Light from a point source placed in air at distance R/2 from the surface falls on it. Find the position and nature of the image formed.$
Refraction at Spherical Surfaces and by Lenses
20 $1{\cdot}6$
Refraction Through a Prism
21 $\sqrt{2}$
Refraction and Total Internal Reflection
25 $\sqrt{2}$
Refraction and Total Internal Reflection
24 $A ray of light is incident at an angle i on a parallel sided glass slab of thickness 'd' and gets refracted into the slab at angle r. Draw a ray diagram to show its path as its emerges out of the slab. Hence, obtain an expression for the lateral shift of the ray. Under what condition will the shift be minimum ?$
Refraction and Total Internal Reflection
25 $(a) A concave mirror has radius of curvature 20 cm. Calculate the distance of an object from the mirror so as to form an image of magnification - 2. Also find the location of the image. (b) If the silver coating around the centre of a concave mirror is removed, will the mirror still form the image of an object ? Justify your answer.$
Reflection by Spherical Mirrors
26 $1{\cdot}75$
Refraction at Spherical Surfaces and by Lenses
26 $(a) When a parallel beam of light enters water surface obliquely at some angle, what is the effect on the width of the beam ? (b) With the help of a ray diagram, show that a straw appears bent when it is partly dipped in water and explain it. (c) Explain the transmission of optical signal through an optical fibre by a diagram.$
Refraction and Total Internal Reflection
27 $1{\cdot}5$
Refraction and Total Internal Reflection
26 $Draw a ray diagram showing the image formation when a concave mirror produces a real, inverted and magnified image of an object and hence obtain the mirror formula.$
Reflection by Spherical Mirrors
A thin lens is a transparent optical medium bounded by two surfaces, at least one of which should be spherical. Applying the formula for image formation by a single spherical surface successively at the two surfaces of a lens, one can obtain the 'lens maker formula' and then the 'lens formula'. A lens has two foci – called 'first focal point' and 'second focal point' of the lens, one on each side.
30 (i) $Consider the arrangement shown in figure. A black vertical arrow and a horizontal thick line with a ball are painted on a glass plate. It serves as the object. When the plate is illuminated, its real image is formed on the screen. Which of the following correctly represents the image formed on the screen ?$
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Refraction at Spherical Surfaces and by Lenses
When light travels from an optically denser medium to an optically rarer medium, at the interface it is partly reflected back into the same medium and partly refracted to the second medium. The angle of incidence corresponding to an angle of refraction $90^{\circ}$ is called the critical angle $(i_c)$ for the given pair of media. This angle is related to the refractive index of medium 1 with respect to medium 2. Refraction of light through a prism involves refraction at two plane interfaces. A relation for the refractive index of the material of the prism can be obtained in terms of the refracting angle of the prism and the angle of minimum deviation. For a thin prism, this relation reduces to a simple equation. Laws of refraction are also valid for refraction of light at a spherical interface. When an object is placed in front of a spherical surface separating two media, its image is formed. A relation between object and image distance, in terms of refractive indices of two media and the radius of curvature of the spherical surface can be obtained. Using this relation for two surfaces of a lens, 'lens maker formula' is obtained.
30 (i) $\left(\dfrac{\mathrm{R}}{\mathrm{H}}\right)$
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Refraction and Total Internal Reflection
A thin lens is a transparent optical medium bounded by two surfaces, at least one of which should be spherical. Applying the formula for image formation by a single spherical surface successively at the two surfaces of a lens, one can obtain the 'lens maker formula' and then the 'lens formula'. A lens has two foci – called 'first focal point' and 'second focal point' of the lens, one on each side.
30 (ii) $Which of the following statements is incorrect ?$
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Refraction at Spherical Surfaces and by Lenses
When light travels from an optically denser medium to an optically rarer medium, at the interface it is partly reflected back into the same medium and partly refracted to the second medium. The angle of incidence corresponding to an angle of refraction $90^{\circ}$ is called the critical angle $(i_c)$ for the given pair of media. This angle is related to the refractive index of medium 1 with respect to medium 2. Refraction of light through a prism involves refraction at two plane interfaces. A relation for the refractive index of the material of the prism can be obtained in terms of the refracting angle of the prism and the angle of minimum deviation. For a thin prism, this relation reduces to a simple equation. Laws of refraction are also valid for refraction of light at a spherical interface. When an object is placed in front of a spherical surface separating two media, its image is formed. A relation between object and image distance, in terms of refractive indices of two media and the radius of curvature of the spherical surface can be obtained. Using this relation for two surfaces of a lens, 'lens maker formula' is obtained.
30 (ii) (a) $60^{\circ}$
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Refraction Through a Prism
A thin lens is a transparent optical medium bounded by two surfaces, at least one of which should be spherical. Applying the formula for image formation by a single spherical surface successively at the two surfaces of a lens, one can obtain the 'lens maker formula' and then the 'lens formula'. A lens has two foci – called 'first focal point' and 'second focal point' of the lens, one on each side.
30 (iii) (a) $A convex lens of focal length 'f' is cut into two equal parts perpendicular to the principal axis. The focal length of each part will be :$
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Refraction at Spherical Surfaces and by Lenses
When light travels from an optically denser medium to an optically rarer medium, at the interface it is partly reflected back into the same medium and partly refracted to the second medium. The angle of incidence corresponding to an angle of refraction $90^{\circ}$ is called the critical angle $(i_c)$ for the given pair of media. This angle is related to the refractive index of medium 1 with respect to medium 2. Refraction of light through a prism involves refraction at two plane interfaces. A relation for the refractive index of the material of the prism can be obtained in terms of the refracting angle of the prism and the angle of minimum deviation. For a thin prism, this relation reduces to a simple equation. Laws of refraction are also valid for refraction of light at a spherical interface. When an object is placed in front of a spherical surface separating two media, its image is formed. A relation between object and image distance, in terms of refractive indices of two media and the radius of curvature of the spherical surface can be obtained. Using this relation for two surfaces of a lens, 'lens maker formula' is obtained.
30 (ii) (b) $1{\cdot}52$
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Refraction Through a Prism
A thin lens is a transparent optical medium bounded by two surfaces, at least one of which should be spherical. Applying the formula for image formation by a single spherical surface successively at the two surfaces of a lens, one can obtain the 'lens maker formula' and then the 'lens formula'. A lens has two foci – called 'first focal point' and 'second focal point' of the lens, one on each side.
30 (iii) (b) $If an object in case (i) above is 20 cm from the lens and the screen is 50 cm away from the object, the focal length of the lens used is$
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Refraction at Spherical Surfaces and by Lenses
When light travels from an optically denser medium to an optically rarer medium, at the interface it is partly reflected back into the same medium and partly refracted to the second medium. The angle of incidence corresponding to an angle of refraction $90^{\circ}$ is called the critical angle $(i_c)$ for the given pair of media. This angle is related to the refractive index of medium 1 with respect to medium 2. Refraction of light through a prism involves refraction at two plane interfaces. A relation for the refractive index of the material of the prism can be obtained in terms of the refracting angle of the prism and the angle of minimum deviation. For a thin prism, this relation reduces to a simple equation. Laws of refraction are also valid for refraction of light at a spherical interface. When an object is placed in front of a spherical surface separating two media, its image is formed. A relation between object and image distance, in terms of refractive indices of two media and the radius of curvature of the spherical surface can be obtained. Using this relation for two surfaces of a lens, 'lens maker formula' is obtained.
30 (iii) $1{\cdot}5$
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Refraction at Spherical Surfaces and by Lenses
A thin lens is a transparent optical medium bounded by two surfaces, at least one of which should be spherical. Applying the formula for image formation by a single spherical surface successively at the two surfaces of a lens, one can obtain the 'lens maker formula' and then the 'lens formula'. A lens has two foci – called 'first focal point' and 'second focal point' of the lens, one on each side.
30 (iv) $\mathrm{X_1}$
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Refraction at Spherical Surfaces and by Lenses
When light travels from an optically denser medium to an optically rarer medium, at the interface it is partly reflected back into the same medium and partly refracted to the second medium. The angle of incidence corresponding to an angle of refraction $90^{\circ}$ is called the critical angle $(i_c)$ for the given pair of media. This angle is related to the refractive index of medium 1 with respect to medium 2. Refraction of light through a prism involves refraction at two plane interfaces. A relation for the refractive index of the material of the prism can be obtained in terms of the refracting angle of the prism and the angle of minimum deviation. For a thin prism, this relation reduces to a simple equation. Laws of refraction are also valid for refraction of light at a spherical interface. When an object is placed in front of a spherical surface separating two media, its image is formed. A relation between object and image distance, in terms of refractive indices of two media and the radius of curvature of the spherical surface can be obtained. Using this relation for two surfaces of a lens, 'lens maker formula' is obtained.
30 (iv) $1{\cdot}5$
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Refraction at Spherical Surfaces and by Lenses
32 (a) $1{\cdot}5$
Optical Instruments
33 (a) $45^\circ$
Reflection by Spherical Mirrors
33 (a) $(i) Draw a ray diagram of a reflecting telescope (Cassegrain) and explain the formation of image. State two important advantages that a reflecting telescope has over a refracting telescope. (ii) In a refracting telescope, the focal length of the objective is 50 times the focal length of the eyepiece. When the final image is formed at infinity, the length of the tube is 102 cm. Find the focal lengths of the two lenses.$
Optical Instruments
33 (a) $\sqrt{3}$
Refraction at Spherical Surfaces and by Lenses
33 (a) $(i) Explain with the help of a labelled ray diagram the formation of final image by an astronomical telescope at infinity. Write the expression for its magnifying power. (ii) The total magnification produced by a compound microscope is 20. The magnification produced by the eyepiece is 5. When the microscope is focussed on a certain object, the distance between the objective and eyepiece is observed to be 14 cm. Calculate the focal lengths of the objective and the eyepiece. (Given that the least distance of distinct vision = 25 cm)$
Optical Instruments
33 (b) $n_1$
Optical Instruments

2024

40 q

7 $The focal lengths of the objective and the eyepiece of a compound microscope are 1 cm and 2 cm respectively. If the tube length of the microscope is 10 cm, the magnification obtained by the microscope for most suitable viewing by relaxed eye is :$
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Optical Instruments
12 $A point object is kept 60 cm in front of a spherical convex surface (n = 1.5, radius of curvature 40 cm). The image formed is$
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Refraction at Spherical Surfaces and by Lenses
Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
16 $Assertion (A) : Plane and convex mirrors cannot produce real images under any circumstance. Reason (R) : A virtual image cannot serve as an object to produce a real image.$
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Reflection by Spherical Mirrors
Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
16 $Assertion (A) : The magnifying power of a compound microscope is negative. Reason (R) : The final image formed is erect with respect to the object.$
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Optical Instruments
Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
16 $Assertion (A) : A convex lens, when immersed in a liquid, disappears. Reason (R) : The refractive indices of material of the lens and the liquid are equal.$
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Refraction at Spherical Surfaces and by Lenses
18 $The magnifying power of an astronomical telescope is 24. In normal adjustment, distance between its two lenses is 150 cm. Find the focal length of the objective lens.$
Optical Instruments
19 $\mu$
Refraction Through a Prism
18 (b) $1{\cdot}4$
Refraction at Spherical Surfaces and by Lenses
19 $Explain the following : (a) For a simple microscope, the angular size of the object equals the angular size of the image. Yet it offers magnification. (b) Both plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances ?$
Optical Instruments
19 $1{\cdot}52$
Refraction at Spherical Surfaces and by Lenses
19 $A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. Calculate its magnifying power in normal adjustment and the distance of the image formed by the objective.$
Optical Instruments
19 $A thin converging lens of focal length 10 cm is placed coaxially in contact with a thin diverging lens of focal length 15 cm. How will the combination behave ? Justify your answer.$
Refraction at Spherical Surfaces and by Lenses
19 $An object is placed 30 cm in front of a concave mirror of radius of curvature 40 cm. Find the (i) position of the image formed and (ii) magnification of the image.$
Reflection by Spherical Mirrors
19 $The radius of curvature of a convex mirror is 30 cm. It forms an image of an object which is half the size of the object. Find the separation between the object and the image.$
Reflection by Spherical Mirrors
21 (a) $An air bubble is trapped at point B (CB = 20 cm) in a glass sphere of radius 40 cm and refractive index 1.5 as shown in figure. Find the nature and position of the image of the bubble as seen by an observer at point P.$
Refraction at Spherical Surfaces and by Lenses
21 (b) $In normal adjustment, for a refracting telescope, the distance between objective and eye piece lens is 1.00 m. If the magnifying power of the telescope is 19, find the focal length of the objective and the eyepiece lens.$
Optical Instruments
A lens is a transparent medium bounded by two surfaces, with one or both surfaces being spherical. The focal length of a lens is determined by the radii of curvature of its two surfaces and the refractive index of its medium with respect to that of the surrounding medium. The power of a lens is reciprocal of its focal length. If a number of lenses are kept in contact, the power of the combination is the algebraic sum of the powers of the individual lenses.
29 (i) $A double-convex lens, with each face having same radius of curvature R, is made of glass of refractive index n. Its power is :$
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Refraction at Spherical Surfaces and by Lenses
A lens is a transparent medium bounded by two surfaces, with one or both surfaces being spherical. The focal length of a lens is determined by the radii of curvature of its two surfaces and the refractive index of its medium with respect to that of the surrounding medium. The power of a lens is reciprocal of its focal length. If a number of lenses are kept in contact, the power of the combination is the algebraic sum of the powers of the individual lenses.
29 (ii) $A double-convex lens of power P, with each face having same radius of curvature, is cut into two equal parts perpendicular to its principal axis. The power of one part of the lens will be :$
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Refraction at Spherical Surfaces and by Lenses
A lens is a transparent medium bounded by two surfaces, with one or both surfaces being spherical. The focal length of a lens is determined by the radii of curvature of its two surfaces and the refractive index of its medium with respect to that of the surrounding medium. The power of a lens is reciprocal of its focal length. If a number of lenses are kept in contact, the power of the combination is the algebraic sum of the powers of the individual lenses.
29 (iii) $The above two parts are kept in contact with each other as shown in the figure. The power of the combination will be :$
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Refraction at Spherical Surfaces and by Lenses
A lens is a transparent medium bounded by two surfaces, with one or both surfaces being spherical. The focal length of a lens is determined by the radii of curvature of its two surfaces and the refractive index of its medium with respect to that of the surrounding medium. The power of a lens is reciprocal of its focal length. If a number of lenses are kept in contact, the power of the combination is the algebraic sum of the powers of the individual lenses.
29 (iv) (a) $A double-convex lens of power P, with each face having same radius of curvature, is cut along its principal axis. The two parts are arranged as shown in the figure. The power of the combination will be :$
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Refraction at Spherical Surfaces and by Lenses
A lens is a transparent medium bounded by two surfaces, with one or both surfaces being spherical. The focal length of a lens is determined by the radii of curvature of its two surfaces and the refractive index of its medium with respect to that of the surrounding medium. The power of a lens is reciprocal of its focal length. If a number of lenses are kept in contact, the power of the combination is the algebraic sum of the powers of the individual lenses.
29 (iv) (b) $Two convex lenses of focal lengths 60 cm and 20 cm are held coaxially in contact with each other. The power of the combination is :$
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Refraction at Spherical Surfaces and by Lenses
A prism is an optical medium bounded by three refracting plane surfaces. A ray of light suffers successive refractions on passing through its two surfaces and deviates by a certain angle from its original path. The refractive index of the material of the prism is given by $\mu = \sin\left(\frac{A + \delta m}{2}\right) / \sin\frac{A}{2}$ . If the angle of incidence on the second surface is greater than an angle called critical angle, the ray will not be refracted from the second surface and is totally internally reflected.
30 (i) $\theta_1$
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Refraction and Total Internal Reflection
When a ray of light propagates from a denser medium to a rarer medium, it bends away from the normal. When the incident angle is increased, the refracted ray deviates more from the normal. For a particular angle of incidence in the denser medium, the refracted ray just grazes the interface of the two surfaces. This angle of incidence is called the critical angle for the pair of media involved.
30 (i) $For a ray incident at the critical angle, the angle of reflection is :$
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Refraction and Total Internal Reflection
A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Applying the formula of image formation by a single spherical surface successively at the two surfaces of a thin lens, a formula known as lens maker's formula and hence the basic lens formula can be obtained. The focal length (or power) of a lens depends on the radii of its surfaces and the refractive index of its material with respect to the surrounding medium. The refractive index of a material depends on the wavelength of light used. Combination of lenses helps us to obtain diverging or converging lenses of desired power and magnification.
30 (i) $A thin converging lens of focal length 20 cm and a thin diverging lens of focal length 15 cm are placed coaxially in contact. The power of the combination is$
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Refraction at Spherical Surfaces and by Lenses
When a ray of light propagates from a denser medium to a rarer medium, it bends away from the normal. When the incident angle is increased, the refracted ray deviates more from the normal. For a particular angle of incidence in the denser medium, the refracted ray just grazes the interface of the two surfaces. This angle of incidence is called the critical angle for the pair of media involved.
30 (ii) $\left(n = \dfrac{4}{3}\right)$
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Refraction and Total Internal Reflection
A prism is an optical medium bounded by three refracting plane surfaces. A ray of light suffers successive refractions on passing through its two surfaces and deviates by a certain angle from its original path. The refractive index of the material of the prism is given by $\mu = \sin\left(\frac{A + \delta m}{2}\right) / \sin\frac{A}{2}$ . If the angle of incidence on the second surface is greater than an angle called critical angle, the ray will not be refracted from the second surface and is totally internally reflected.
30 (ii) $\lambda$
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Refraction and Total Internal Reflection
A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Applying the formula of image formation by a single spherical surface successively at the two surfaces of a thin lens, a formula known as lens maker's formula and hence the basic lens formula can be obtained. The focal length (or power) of a lens depends on the radii of its surfaces and the refractive index of its material with respect to the surrounding medium. The refractive index of a material depends on the wavelength of light used. Combination of lenses helps us to obtain diverging or converging lenses of desired power and magnification.
30 (ii) $\left(\dfrac{4}{3}\right)\mathrm{R}$
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Refraction at Spherical Surfaces and by Lenses
A prism is an optical medium bounded by three refracting plane surfaces. A ray of light suffers successive refractions on passing through its two surfaces and deviates by a certain angle from its original path. The refractive index of the material of the prism is given by $\mu = \sin\left(\frac{A + \delta m}{2}\right) / \sin\frac{A}{2}$ . If the angle of incidence on the second surface is greater than an angle called critical angle, the ray will not be refracted from the second surface and is totally internally reflected.
30 (iii) (a) $The critical angle for a ray of light passing from glass to water is minimum for$
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Refraction and Total Internal Reflection
A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Applying the formula of image formation by a single spherical surface successively at the two surfaces of a thin lens, a formula known as lens maker's formula and hence the basic lens formula can be obtained. The focal length (or power) of a lens depends on the radii of its surfaces and the refractive index of its material with respect to the surrounding medium. The refractive index of a material depends on the wavelength of light used. Combination of lenses helps us to obtain diverging or converging lenses of desired power and magnification.
30 (iii) $The focal length of an equiconvex lens$
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Refraction at Spherical Surfaces and by Lenses
When a ray of light propagates from a denser medium to a rarer medium, it bends away from the normal. When the incident angle is increased, the refracted ray deviates more from the normal. For a particular angle of incidence in the denser medium, the refracted ray just grazes the interface of the two surfaces. This angle of incidence is called the critical angle for the pair of media involved.
30 (iii) (a) $30^\circ$
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Refraction and Total Internal Reflection
A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Applying the formula of image formation by a single spherical surface successively at the two surfaces of a thin lens, a formula known as lens maker's formula and hence the basic lens formula can be obtained. The focal length (or power) of a lens depends on the radii of its surfaces and the refractive index of its material with respect to the surrounding medium. The refractive index of a material depends on the wavelength of light used. Combination of lenses helps us to obtain diverging or converging lenses of desired power and magnification.
30 (iv) (a) $A thin convex lens L of focal length 10 cm and a concave mirror M of focal length 15 cm are placed coaxially 40 cm apart as shown in figure. A beam of light coming parallel to the principal axis is incident on the lens. The final image will be formed at a distance of$
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Refraction at Spherical Surfaces and by Lenses
When a ray of light propagates from a denser medium to a rarer medium, it bends away from the normal. When the incident angle is increased, the refracted ray deviates more from the normal. For a particular angle of incidence in the denser medium, the refracted ray just grazes the interface of the two surfaces. This angle of incidence is called the critical angle for the pair of media involved.
30 (iii) (b) $2 \times 10^8$
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Refraction and Total Internal Reflection
A prism is an optical medium bounded by three refracting plane surfaces. A ray of light suffers successive refractions on passing through its two surfaces and deviates by a certain angle from its original path. The refractive index of the material of the prism is given by $\mu = \sin\left(\frac{A + \delta m}{2}\right) / \sin\frac{A}{2}$ . If the angle of incidence on the second surface is greater than an angle called critical angle, the ray will not be refracted from the second surface and is totally internally reflected.
30 (iii) (b) $r_R$
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Refraction Through a Prism
A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Applying the formula of image formation by a single spherical surface successively at the two surfaces of a thin lens, a formula known as lens maker's formula and hence the basic lens formula can be obtained. The focal length (or power) of a lens depends on the radii of its surfaces and the refractive index of its material with respect to the surrounding medium. The refractive index of a material depends on the wavelength of light used. Combination of lenses helps us to obtain diverging or converging lenses of desired power and magnification.
30 (iv) (b) $L_1$
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Refraction at Spherical Surfaces and by Lenses
When a ray of light propagates from a denser medium to a rarer medium, it bends away from the normal. When the incident angle is increased, the refracted ray deviates more from the normal. For a particular angle of incidence in the denser medium, the refracted ray just grazes the interface of the two surfaces. This angle of incidence is called the critical angle for the pair of media involved.
30 (iv) $\theta$
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Refraction Through a Prism
A prism is an optical medium bounded by three refracting plane surfaces. A ray of light suffers successive refractions on passing through its two surfaces and deviates by a certain angle from its original path. The refractive index of the material of the prism is given by $\mu = \sin\left(\frac{A + \delta m}{2}\right) / \sin\frac{A}{2}$ . If the angle of incidence on the second surface is greater than an angle called critical angle, the ray will not be refracted from the second surface and is totally internally reflected.
30 (iv) $\sqrt{2}$
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Refraction Through a Prism
31 (a) $(i) Draw a ray diagram for the formation of the image of an object by a convex mirror. Hence, obtain the mirror equation. (ii) Why are multi-component lenses used for both the objective and the eyepiece in optical instruments ? (iii) The magnification of a small object produced by a compound microscope is 200. The focal length of the eyepiece is 2 cm and the final image is formed at infinity. Find the magnification produced by the objective.$
Optical Instruments
33 (a) $(\delta)$
Refraction Through a Prism
33 (a) $\delta$
Refraction Through a Prism
33 (b) $(i) Draw a labelled ray diagram of a compound microscope showing image formation at least distance of distinct vision. Derive an expression for its magnifying power. (ii) A telescope consists of two lenses of focal length 100 cm and 5 cm. Find the magnifying power when the final image is formed at infinity.$
Optical Instruments

2023

35 q

3 $The minimum distance between an object and its real image formed by a convex lens of focal length f is :$
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Refraction at Spherical Surfaces and by Lenses
8 $A ray of monochromatic light propagating in air, is incident on the surface of water. Which of the following will be the same for the reflected and refracted rays ?$
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Refraction and Total Internal Reflection
9 $For a concave mirror of focal length 'f', the minimum distance between the object and its real image is :$
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Reflection by Spherical Mirrors
12 $A ray of light travels a distance of 12.0 m in a transparent sheet in 60 ns. The refractive index of the sheet is$
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Refraction and Total Internal Reflection
13 $Which of the following pairs of media has the least value of critical angle ?$
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Refraction and Total Internal Reflection
19 $\dfrac{25}{6}$
Refraction at Spherical Surfaces and by Lenses
21 $In the given figure the radius of curvature of curved face in the plano-convex and the plano-concave lens is 15 cm each. The refractive index of the material of the lenses is 1.5. Find the final position of the image formed.$
Refraction at Spherical Surfaces and by Lenses
21 (b) $Why is a reflecting telescope preferred over a refracting telescope ? Justify your answer giving two reasons.$
Optical Instruments
22 $\sqrt{2}$
Refraction and Total Internal Reflection
23 $The power of a thin lens is +5 D. When it is immersed in a liquid, it behaves like a concave lens of focal length 100 cm. Calculate the refractive index of the liquid. Given refractive index of glass = 1.5.$
Refraction at Spherical Surfaces and by Lenses
24 $1{\cdot}5$
Refraction at Spherical Surfaces and by Lenses
25 $A point object in air is placed symmetrically at a distance of 60 cm in front of a concave spherical surface of refractive index 1.5. If the radius of curvature of the surface is 20 cm, find the position of the image formed.$
Refraction at Spherical Surfaces and by Lenses
26 $\delta\mathrm{m}$
Refraction Through a Prism
27 $\mu$
Refraction Through a Prism
29 $Define critical angle for a given pair of media and total internal reflection. Obtain the relation between the critical angle and refractive index of the medium.$
Refraction and Total Internal Reflection
32 (a) $\mathrm{L_1}$
Optical Instruments
32 (b) $(\delta_m)$
Refraction Through a Prism
33 (a) $1{\cdot}8$
Reflection by Spherical Mirrors
33 (a) $(i) Draw a ray diagram to show the working of a compound microscope. Obtain the expression for the total magnification for the final image to be formed at the near point. (ii) In a compound microscope an object is placed at a distance of 1.5 cm from the objective of focal length 1.25 cm. If the eye-piece has a focal length of 5 cm and the final image is formed at the near point, find the magnifying power of the microscope.$
Optical Instruments
33 (b) $(i) Draw a ray diagram for the formation of image of an object by an astronomical telescope, in normal adjustment. Obtain the expression for its magnifying power. (ii) The magnifying power of an astronomical telescope in normal adjustment is 2.9 and the objective and the eyepiece are separated by a distance of 150 cm. Find the focal lengths of the two lenses.$
Optical Instruments
33 (b) $(i) Draw a labelled ray diagram showing the image formation by a refracting telescope. Define its magnifying power. Write two limitations of a refracting telescope over a reflecting telescope. (ii) The focal lengths of the objective and the eye-piece of a compound microscope are 1.0 cm and 2.5 cm respectively. Find the tube length of the microscope for obtaining a magnification of 300.$
Optical Instruments
33 (b) $\mathrm{n_1}$
Refraction at Spherical Surfaces and by Lenses
33 (b) $(\mu)$
Refraction Through a Prism
A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Considering image formation by a single spherical surface successively at the two surfaces of a lens, lens maker's formula is obtained. It is useful to design lenses of desired focal length using surfaces of suitable radii of curvature. This formula helps us obtain a relation between u, v and f for a lens. Lenses form images of objects and they are used in a number of optical devices, for example microscopes and telescopes.
34 (i) $An object AB is kept in front of a composite convex lens, as shown in figure. Will the lens produce one image ? If not, explain.$
Refraction at Spherical Surfaces and by Lenses
A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Considering image formation by a single spherical surface successively at the two surfaces of a lens, lens maker's formula is obtained. It is useful to design lenses of desired focal length using surfaces of suitable radii of curvature. This formula helps us obtain a relation between u, v and f for a lens. Lenses form images of objects and they are used in a number of optical devices, for example microscopes and telescopes.
34 (ii) $A real image of an object formed by a convex lens is observed on a screen. If the screen is removed, will the image still be formed ? Explain.$
Refraction at Spherical Surfaces and by Lenses
A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Considering image formation by a single spherical surface successively at the two surfaces of a lens, lens maker's formula is obtained. It is useful to design lenses of desired focal length using surfaces of suitable radii of curvature. This formula helps us obtain a relation between u, v and f for a lens. Lenses form images of objects and they are used in a number of optical devices, for example microscopes and telescopes.
34 (iii) (a) $A double convex lens is made of glass of refractive index 1.55 with both faces of the same radius of curvature. Find the radius of curvature required if focal length is 20 cm.$
Refraction at Spherical Surfaces and by Lenses
A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Considering image formation by a single spherical surface successively at the two surfaces of a lens, lens maker's formula is obtained. It is useful to design lenses of desired focal length using surfaces of suitable radii of curvature. This formula helps us obtain a relation between u, v and f for a lens. Lenses form images of objects and they are used in a number of optical devices, for example microscopes and telescopes.
34 (iii) (b) $Two convex lenses A and B of focal lengths 15 cm and 10 cm respectively are placed coaxially 'd' distance apart. A point object is kept at a distance of 30 cm in front of lens A. Find the value of 'd' so that the rays emerging from lens B are parallel to its principal axis.$
Refraction at Spherical Surfaces and by Lenses
Strontium titanate is a rare oxide — a natural mineral found in Siberia. It is used as a substitute for diamond because its refractive index and critical angle are $2{\cdot}41$ and $24{\cdot}5°$ , respectively, which are approximately equal to the refractive index and critical angle of diamond. It has all the properties of diamond. Even an expert jeweller is unable to differentiate between diamond and strontium titanate. A ray of light is incident normally on one face of an equilateral triangular prism ABC made of strontium titanate.
35 (a) $Trace the path of the ray showing its passage through the prism.$
Refraction and Total Internal Reflection
The lens maker's formula is useful to design lenses of desired focal lengths using surfaces of suitable radii of curvature. The focal length also depends on the refractive index of the material of the lens and the surrounding medium. The refractive index depends on the wavelength of the light used. The power of a lens is related to its focal length.
35 (a) $How will the power of a lens be affected with an increase of wavelength of light ?$
Refraction at Spherical Surfaces and by Lenses
The lens maker's formula is useful to design lenses of desired focal lengths using surfaces of suitable radii of curvature. The focal length also depends on the refractive index of the material of the lens and the surrounding medium. The refractive index depends on the wavelength of the light used. The power of a lens is related to its focal length.
35 (b) $\mu$
Refraction at Spherical Surfaces and by Lenses
Strontium titanate is a rare oxide — a natural mineral found in Siberia. It is used as a substitute for diamond because its refractive index and critical angle are $2{\cdot}41$ and $24{\cdot}5°$ , respectively, which are approximately equal to the refractive index and critical angle of diamond. It has all the properties of diamond. Even an expert jeweller is unable to differentiate between diamond and strontium titanate. A ray of light is incident normally on one face of an equilateral triangular prism ABC made of strontium titanate.
35 (b) $Find the velocity of light through the prism.$
Refraction and Total Internal Reflection
The lens maker's formula is useful to design lenses of desired focal lengths using surfaces of suitable radii of curvature. The focal length also depends on the refractive index of the material of the lens and the surrounding medium. The refractive index depends on the wavelength of the light used. The power of a lens is related to its focal length.
35 (c) $\mu = 1{\cdot}5$
Refraction at Spherical Surfaces and by Lenses
Strontium titanate is a rare oxide — a natural mineral found in Siberia. It is used as a substitute for diamond because its refractive index and critical angle are $2{\cdot}41$ and $24{\cdot}5°$ , respectively, which are approximately equal to the refractive index and critical angle of diamond. It has all the properties of diamond. Even an expert jeweller is unable to differentiate between diamond and strontium titanate. A ray of light is incident normally on one face of an equilateral triangular prism ABC made of strontium titanate.
35 (c) $Briefly explain two applications of total internal reflection.$
Refraction and Total Internal Reflection
The lens maker's formula is useful to design lenses of desired focal lengths using surfaces of suitable radii of curvature. The focal length also depends on the refractive index of the material of the lens and the surrounding medium. The refractive index depends on the wavelength of the light used. The power of a lens is related to its focal length.
35 (c) OR $An object is placed in front of a lens which forms its erect image of magnification 3. The power of the lens is 5 D. Calculate the distance of the object and the image from the lens.$
Refraction at Spherical Surfaces and by Lenses
Strontium titanate is a rare oxide — a natural mineral found in Siberia. It is used as a substitute for diamond because its refractive index and critical angle are $2{\cdot}41$ and $24{\cdot}5°$ , respectively, which are approximately equal to the refractive index and critical angle of diamond. It has all the properties of diamond. Even an expert jeweller is unable to differentiate between diamond and strontium titanate. A ray of light is incident normally on one face of an equilateral triangular prism ABC made of strontium titanate.
35 (c) OR $Define total internal reflection of light. Give two conditions for it.$
Refraction and Total Internal Reflection

2022

39 q

5 $({}_{a}\mu_{g} = 1.5)$
Refraction at Spherical Surfaces and by Lenses
6 $An equiconvex lens forms a two times enlarged real image when an object is kept 16 cm from it. The lens is cut into two identical plano-convex lenses. If the object is again kept 16 cm in front of one of these lenses, then find the nature and position of the image formed.$
Refraction at Spherical Surfaces and by Lenses
5 $(a) State the conditions for total internal reflection to take place. (b) A tank is filled with a transparent liquid to height 'H'. A coin suspended by a thread in the liquid is gradually lowered till it touches the bottom. The apparent depth is determined corresponding to different positions of the coin. (i) Plot a graph showing variation of the apparent depth with the real depth of the coin. (ii) What is the physical significance of the slope of the graph ?$
Refraction and Total Internal Reflection
6 $With the help of a ray diagram, show how a compound microscope forms a magnified image of a tiny object, at least distance of distinct vision. Hence derive an expression for the magnification produced by it.$
Optical Instruments
7 $Explain with the help of a suitable diagram, the phenomenon on which an optical fibre works. Mention any two uses of optical fibres.$
Refraction and Total Internal Reflection
7 $\sqrt{2}$
Refraction Through a Prism
6 (a) $Draw a labelled ray diagram showing the formation of an image by an astronomical refracting telescope in normal adjustment. Hence, obtain the expression for its magnifying power.$
Optical Instruments
8 (a) $41.1^\circ$
Refraction and Total Internal Reflection
8 (a) $6{\cdot}0$
Optical Instruments
8 (a) $(i) Define SI unit of power of a lens. (ii) A plano convex lens is made of glass of refractive index 1.5. The radius of curvature of the convex surface is 25 cm. (ii.i) Calculate the focal length of the lens. (ii.ii) If an object is placed 50 cm in front of the lens, find the nature and position of the image formed.$
Refraction at Spherical Surfaces and by Lenses
8 (b) $\mu_1$
Refraction at Spherical Surfaces and by Lenses
7 $\mu = 1{\cdot}5$
Refraction at Spherical Surfaces and by Lenses
8 (b) $(a) An object is placed in front of a converging lens. Obtain the conditions under which the magnification produced by the lens is (i) negative and (ii) positive. (b) A point object is placed at O in front of a glass sphere as shown in figure. Show the formation of image by the sphere.$
Refraction at Spherical Surfaces and by Lenses
8 (b) $3{\cdot}0$
Optical Instruments
10 $\sqrt{2}$
Refraction Through a Prism
10 $45^\circ$
Refraction Through a Prism
10 $+5.0$
Refraction at Spherical Surfaces and by Lenses
10 $\dfrac{4}{3}$
Refraction and Total Internal Reflection
11 $\textcircled{1}$
Refraction and Total Internal Reflection
11 (b) $With the help of a ray diagram explain the working of a reflecting telescope. Mention two advantages of a reflecting telescope over a refracting telescope.$
Optical Instruments
11 (b) $\angle\delta = \angle i + \angle e - \angle A$
Refraction Through a Prism
11 $\sqrt{3}$
Refraction Through a Prism
11 $\left(\mu = \frac{4}{3}\right)$
Refraction and Total Internal Reflection
11 $\sqrt{2}$
Refraction Through a Prism
A compound microscope consists of two converging lenses. One of them, of smaller aperture and smaller focal length is called objective and the other of slightly larger aperture and slightly larger focal length is called eye-piece. Both the lenses are fitted in a tube with an arrangement to vary the distance between them. A tiny object is placed in front of the objective at a distance slightly greater than its focal length. The objective produces the image of the object which acts as an object for the eye-piece. The eye piece, in turn produces the final magnified image.
12 (I) $In a compound microscope the images formed by the objective and the eye-piece are respectively$
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Optical Instruments
A ray of light travels from a denser to a rarer medium. After refraction, it bends away from the normal. When we keep increasing the angle of incidence, the angle of refraction also increases till the refracted ray grazes along the interface of two media. The angle of incidence for which it happens is called critical angle. If the angle of incidence is increased farther the ray will not emerge and it will be reflected back in the denser medium. This phenomenon is called total internal reflection of light.
12 (i) $18^\circ$
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Refraction and Total Internal Reflection
Two transparent media of refractive indices $\mathrm{n_1}$ and $\mathrm{n_2}$ are separated by a spherical transparent surface. The rays of light incident on the surface get refracted into the medium on the other side. The laws of refraction are valid at each point of the spherical surface. A lens is a transparent optical medium bounded by two surfaces, at least one of which should be spherical. The focal length of a lens is determined by the radii of curvature $(\mathrm{R_1}$ and $\mathrm{R_2})$ of its two surfaces and the refractive index (n) of the medium of the lens with respect to the surrounding medium. Depending on $\mathrm{R_1}$ and $\mathrm{R_2}$ , a lens behaves as a diverging or a converging lens. The ability of a lens to diverge or converge a beam of light incident on it defines its power.
12 (a) $An object is placed at the point B as shown in the figure. The object distance (u) and the image distance (v) are related as$
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Refraction at Spherical Surfaces and by Lenses
A compound microscope consists of two converging lenses. One of them, of smaller aperture and smaller focal length is called objective and the other of slightly larger aperture and slightly larger focal length is called eye-piece. Both the lenses are fitted in a tube with an arrangement to vary the distance between them. A tiny object is placed in front of the objective at a distance slightly greater than its focal length. The objective produces the image of the object which acts as an object for the eye-piece. The eye piece, in turn produces the final magnified image.
12 (II) $The magnification due to a compound microscope does not depend upon$
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Optical Instruments
Two transparent media of refractive indices $\mathrm{n_1}$ and $\mathrm{n_2}$ are separated by a spherical transparent surface. The rays of light incident on the surface get refracted into the medium on the other side. The laws of refraction are valid at each point of the spherical surface. A lens is a transparent optical medium bounded by two surfaces, at least one of which should be spherical. The focal length of a lens is determined by the radii of curvature $(\mathrm{R_1}$ and $\mathrm{R_2})$ of its two surfaces and the refractive index (n) of the medium of the lens with respect to the surrounding medium. Depending on $\mathrm{R_1}$ and $\mathrm{R_2}$ , a lens behaves as a diverging or a converging lens. The ability of a lens to diverge or converge a beam of light incident on it defines its power.
12 (b) $A point object is placed in air at a distance 'R' in front of a convex spherical refracting surface of radius of curvature R. If the medium on the other side of the surface is glass, then the image is :$
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Refraction at Spherical Surfaces and by Lenses
A ray of light travels from a denser to a rarer medium. After refraction, it bends away from the normal. When we keep increasing the angle of incidence, the angle of refraction also increases till the refracted ray grazes along the interface of two media. The angle of incidence for which it happens is called critical angle. If the angle of incidence is increased farther the ray will not emerge and it will be reflected back in the denser medium. This phenomenon is called total internal reflection of light.
12 (ii) $\mu$
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Refraction and Total Internal Reflection
A compound microscope consists of two converging lenses. One of them, of smaller aperture and smaller focal length is called objective and the other of slightly larger aperture and slightly larger focal length is called eye-piece. Both the lenses are fitted in a tube with an arrangement to vary the distance between them. A tiny object is placed in front of the objective at a distance slightly greater than its focal length. The objective produces the image of the object which acts as an object for the eye-piece. The eye piece, in turn produces the final magnified image.
12 (III) $Which of the following is not correct in the context of a compound microscope ?$
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Optical Instruments
A ray of light travels from a denser to a rarer medium. After refraction, it bends away from the normal. When we keep increasing the angle of incidence, the angle of refraction also increases till the refracted ray grazes along the interface of two media. The angle of incidence for which it happens is called critical angle. If the angle of incidence is increased farther the ray will not emerge and it will be reflected back in the denser medium. This phenomenon is called total internal reflection of light.
12 (iii) $For which of the following media, with respect to air, the value of critical angle is maximum ?$
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Refraction and Total Internal Reflection
Two transparent media of refractive indices $\mathrm{n_1}$ and $\mathrm{n_2}$ are separated by a spherical transparent surface. The rays of light incident on the surface get refracted into the medium on the other side. The laws of refraction are valid at each point of the spherical surface. A lens is a transparent optical medium bounded by two surfaces, at least one of which should be spherical. The focal length of a lens is determined by the radii of curvature $(\mathrm{R_1}$ and $\mathrm{R_2})$ of its two surfaces and the refractive index (n) of the medium of the lens with respect to the surrounding medium. Depending on $\mathrm{R_1}$ and $\mathrm{R_2}$ , a lens behaves as a diverging or a converging lens. The ability of a lens to diverge or converge a beam of light incident on it defines its power.
12 (c) $An object is kept at 2F in front of an equiconvex lens. The image formed is :$
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Refraction at Spherical Surfaces and by Lenses
A ray of light travels from a denser to a rarer medium. After refraction, it bends away from the normal. When we keep increasing the angle of incidence, the angle of refraction also increases till the refracted ray grazes along the interface of two media. The angle of incidence for which it happens is called critical angle. If the angle of incidence is increased farther the ray will not emerge and it will be reflected back in the denser medium. This phenomenon is called total internal reflection of light.
12 (iv) $The critical angle for a pair of two media A and B of refractive indices 2.0 and 1.0 respectively is :$
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Refraction and Total Internal Reflection
Two transparent media of refractive indices $\mathrm{n_1}$ and $\mathrm{n_2}$ are separated by a spherical transparent surface. The rays of light incident on the surface get refracted into the medium on the other side. The laws of refraction are valid at each point of the spherical surface. A lens is a transparent optical medium bounded by two surfaces, at least one of which should be spherical. The focal length of a lens is determined by the radii of curvature $(\mathrm{R_1}$ and $\mathrm{R_2})$ of its two surfaces and the refractive index (n) of the medium of the lens with respect to the surrounding medium. Depending on $\mathrm{R_1}$ and $\mathrm{R_2}$ , a lens behaves as a diverging or a converging lens. The ability of a lens to diverge or converge a beam of light incident on it defines its power.
12 (d) $A thin converging lens of focal length 10 cm and a thin diverging lens of focal length 20 cm are placed coaxially in contact. The power of the combination is :$
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Refraction at Spherical Surfaces and by Lenses
A compound microscope consists of two converging lenses. One of them, of smaller aperture and smaller focal length is called objective and the other of slightly larger aperture and slightly larger focal length is called eye-piece. Both the lenses are fitted in a tube with an arrangement to vary the distance between them. A tiny object is placed in front of the objective at a distance slightly greater than its focal length. The objective produces the image of the object which acts as an object for the eye-piece. The eye piece, in turn produces the final magnified image.
12 (IV) $A compound microscope consists of an objective of 10X and an eye-piece of 20X. The magnification due to the microscope would be$
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Optical Instruments
A compound microscope consists of two converging lenses. One of them, of smaller aperture and smaller focal length is called objective and the other of slightly larger aperture and slightly larger focal length is called eye-piece. Both the lenses are fitted in a tube with an arrangement to vary the distance between them. A tiny object is placed in front of the objective at a distance slightly greater than its focal length. The objective produces the image of the object which acts as an object for the eye-piece. The eye piece, in turn produces the final magnified image.
12 (V) $The focal lengths of objective and eye-piece of a compound microscope are 1.2 cm and 3.0 cm respectively. The object is placed at a distance of 1.25 cm from the objective. If the final image is formed at infinity, the magnifying power of the microscope would be$
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Optical Instruments
A ray of light travels from a denser to a rarer medium. After refraction, it bends away from the normal. When we keep increasing the angle of incidence, the angle of refraction also increases till the refracted ray grazes along the interface of two media. The angle of incidence for which it happens is called critical angle. If the angle of incidence is increased farther the ray will not emerge and it will be reflected back in the denser medium. This phenomenon is called total internal reflection of light.
12 (v) $30^\circ$
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Refraction and Total Internal Reflection
Two transparent media of refractive indices $\mathrm{n_1}$ and $\mathrm{n_2}$ are separated by a spherical transparent surface. The rays of light incident on the surface get refracted into the medium on the other side. The laws of refraction are valid at each point of the spherical surface. A lens is a transparent optical medium bounded by two surfaces, at least one of which should be spherical. The focal length of a lens is determined by the radii of curvature $(\mathrm{R_1}$ and $\mathrm{R_2})$ of its two surfaces and the refractive index (n) of the medium of the lens with respect to the surrounding medium. Depending on $\mathrm{R_1}$ and $\mathrm{R_2}$ , a lens behaves as a diverging or a converging lens. The ability of a lens to diverge or converge a beam of light incident on it defines its power.
12 (e) $An equiconcave lens of focal length 'f' is cut into two identical parts along the dotted line as shown in the figure. The focal length of each part will be :$
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Refraction at Spherical Surfaces and by Lenses

The 10 board questions to practise first

The questions the board asked again come first, most asked first. Each one says how often and when.

Question 1
Asked 3 times: 2024*, 2025*, 2026 (* = numbers or wording changed that year)
21 $1{\cdot}5$
Question 2
Asked 2 times: 2022, 2026
20 $Draw a labelled ray diagram of an astronomical telescope when final image is formed at infinity. Write the expression for its magnifying power.$
Question 3
Asked 2 times: 2022, 2026
28 $Draw a labelled ray diagram showing the formation of image by a compound microscope when final image is formed at least distance of distinct vision. Derive an expression for its magnifying power for this case.$
Question 4
Asked 2 times: 2025*, 2026 (* = numbers or wording changed that year)
19 $\sqrt{2}$
Question 5
Asked 2 times: 2025*, 2026 (* = numbers or wording changed that year)
19 $12{\cdot}5$
Question 6
Asked 2 times: 2024*, 2026 (* = numbers or wording changed that year)
20 $1{\cdot}5$
Question 7
Asked 2 times: 2023*, 2025 (* = numbers or wording changed that year)
19 $1{\cdot}55$
Question 8
Asked 2 times: 2022*, 2023 (* = numbers or wording changed that year)
25 $A point object in air is placed symmetrically at a distance of 60 cm in front of a concave spherical surface of refractive index 1.5. If the radius of curvature of the surface is 20 cm, find the position of the image formed.$
Question 9
This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2025
32 (a) $1{\cdot}5$
Question 10
This type asked 5 times: 2022, 2023, 2024, 2025, 2026. This one: 2026
7 $Light from a small object in air falls on a spherical glass surface (n = 1.5) of radius of curvature R. A real image of the object will be formed if the object distance u is related to R as :$
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Worked Examples

Solved Examples

Exercises

What the board has asked from this chapter

2026

2025

2024

2023

2022

The 10 board questions to practise first

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10