Science · Textbook solutions

Light — Reflection and Refraction

Every textbook question in book order, plus the board's past questions. · 37 questions

9.2 Spherical Mirrors

4 q

Questions

Practice · 4

IT 9.1 Q1 $Define the principal focus of a concave mirror.$
IT 9.1 Q2 $The radius of curvature of a spherical mirror is 20 cm. What is its focal length?$
IT 9.1 Q3 $Name a mirror that can give an erect and enlarged image of an object.$
IT 9.1 Q4 $Why do we prefer a convex mirror as a rear-view mirror in vehicles?$

9.2.4 Mirror Formula and Magnification

4 q

Solved Examples

Worked · 2

9.2 Eg.1 $A convex mirror used for rear-view on an automobile has a radius of curvature of 3.00 m. If a bus is located at 5.00 m from this mirror, find the position, nature and size of the image.$
9.2 Eg.2 $An object, 4.0 cm in size, is placed at 25.0 cm in front of a concave mirror of focal length 15.0 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Find the nature and the size of the image.$

Questions

Practice · 2

IT 9.2 Q1 $Find the focal length of a convex mirror whose radius of curvature is 32 cm.$
IT 9.2 Q2 $A concave mirror produces three times magnified (enlarged) real image of an object placed at 10 cm in front of it. Where is the image located?$

9.3 Refraction of Light

5 q

Questions

Practice · 5

IT 9.3 Q1 $A ray of light travelling in air enters obliquely into water. Does the light ray bend towards the normal or away from the normal? Why?$
IT 9.3 Q2 $Light enters from air to glass having refractive index 1.50. What is the speed of light in the glass? The speed of light in vacuum is 3 × 10⁸ m s⁻¹.$
IT 9.3 Q3 $Find out, from Table 9.3, the medium having highest optical density. Also find the medium with lowest optical density.$
IT 9.3 Q4 $You are given kerosene, turpentine and water. In which of these does the light travel fastest? Use the information given in Table 9.3.$
IT 9.3 Q5 $The refractive index of diamond is 2.42. What is the meaning of this statement?$

9.3.7-9.3.8 Lens Formula, Magnification and Power of a Lens

5 q

Solved Examples

Worked · 2

9.4 Eg.3 $A concave lens has focal length of 15 cm. At what distance should the object from the lens be placed so that it forms an image at 10 cm from the lens? Also, find the magnification produced by the lens.$
9.4 Eg.4 $A 2.0 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 10 cm. The distance of the object from the lens is 15 cm. Find the nature, position and size of the image. Also find its magnification.$

Questions

Practice · 3

IT 9.4 Q1 $Define 1 dioptre of power of a lens.$
IT 9.4 Q2 $A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also, find the power of the lens.$
IT 9.4 Q3 $Find the power of a concave lens of focal length 2 m.$

Exercises

19 q

Ex 9 Q1 $Which one of the following materials cannot be used to make a lens?$
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Ex 9 Q2 $The image formed by a concave mirror is observed to be virtual, erect and larger than the object. Where should be the position of the object?$
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Ex 9 Q3 $Where should an object be placed in front of a convex lens to get a real image of the size of the object?$
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Ex 9 Q4 $A spherical mirror and a thin spherical lens have each a focal length of -15 cm. The mirror and the lens are likely to be$
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Ex 9 Q5 $No matter how far you stand from a mirror, your image appears erect. The mirror is likely to be$
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Ex 9 Q6 $Which of the following lenses would you prefer to use while reading small letters found in a dictionary?$
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Ex 9 Q7 $We wish to obtain an erect image of an object, using a concave mirror of focal length 15 cm. What should be the range of distance of the object from the mirror? What is the nature of the image? Is the image larger or smaller than the object? Draw a ray diagram to show the image formation in this case.$
Name the type of mirror used in the following situations. Support your answer with reason.
Ex 9 Q8 (a) $Headlights of a car.$
Name the type of mirror used in the following situations. Support your answer with reason.
Ex 9 Q8 (b) $Side/rear-view mirror of a vehicle.$
Name the type of mirror used in the following situations. Support your answer with reason.
Ex 9 Q8 (c) $Solar furnace.$
Ex 9 Q9 $One-half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object? Verify your answer experimentally. Explain your observations.$
Ex 9 Q10 $An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. Draw the ray diagram and find the position, size and the nature of the image formed.$
Ex 9 Q11 $A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram.$
Ex 9 Q12 $An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image.$
Ex 9 Q13 $The magnification produced by a plane mirror is +1. What does this mean?$
Ex 9 Q14 $An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size.$
Ex 9 Q15 $An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained? Find the size and the nature of the image.$
Ex 9 Q16 $Find the focal length of a lens of power - 2.0 D. What type of lens is this?$
Ex 9 Q17 $A doctor has prescribed a corrective lens of power +1.5 D. Find the focal length of the lens. Is the prescribed lens diverging or converging?$

What the board has asked from this chapter

Questions per paper · 63 papers · 2023 to 2026

2026

35 q

33 $\mathrm{V_A}$
Refractive Index
30 $From the following options choose the one which gives negative magnification greater than one :$
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Mirror Formula and Magnification
30 $Rays from the sun converge at a point 25 cm behind a convex lens. The distance at which an object be placed in front of the lens to get a virtual image, is :$
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Spherical Lenses and Image Formation
30 $A convex lens of focal length 15 cm, is forming a real image. If the size of image is same as the size of object, then position of object and position of image will be, respectively :$
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Spherical Lenses and Image Formation
33 $Draw the ray diagram showing refraction through a glass slab and write the relation between angle of incidence, angle of refraction and refractive index of glass.$
Refraction of Light
34 $Redraw the following ray diagrams in your answer book and show the path of reflected/refracted ray :$
Spherical Mirrors and Image Formation
33 $\sqrt{3}$
Refractive Index
33 $2.25 \times 10^8$
Refractive Index
33 $\sqrt{3} = 1{\cdot}732$
Refractive Index
33 $When an incident ray of light enters in a medium ‘X’ from medium ‘Y’, it bends away from the normal. Comment about the following : (a) Speed of light in medium ‘X’ with respect to the speed of light in medium of ‘Y’. (b) Optical density of medium ‘X’ with respect to the optical density of medium ‘Y’. Give reason for your answer in each case.$
Refractive Index
33 $\sqrt{3}$
Refractive Index
33 $The given figure shows image formation by a lens. Analyse the figure and answer the following questions : (a) What is the type of lens used for image formation in the given ray diagram ? (b) If the real image is formed at a distance of 30 cm from the lens and the size of image is twice the size of the object, then where was the object placed ?$
Lens Formula and Power of a Lens
33 $(a) Define absolute refractive index of an optical medium. (b)Material MediumRefractive IndexA1.50B1.46C1.31D1.77Arrange these material mediums given in the table in increasing order of speed of light through them.$
Refractive Index
33 $+2$
Spherical Lenses and Image Formation
34 $A mirror always forms a virtual, erect and diminished image. Identify the mirror and draw a labelled ray diagram for image formation by this mirror.$
Spherical Mirrors and Image Formation
35 $(a) State the laws which help to find out the angle of incidence and angle of reflection in the ray diagram given above. (b) Find out the angle of incidence and angle of reflection in the given ray diagram.$
Reflection of Light
35 $(a) Observe the given ray diagram and compare : (i) the speed of light in medium A and the speed of light in medium B. (ii) the optical densities of medium B and medium C. (b) Draw a ray diagram for refraction where the optical density of medium ‘A’ becomes equal to the optical density of medium ‘C’ and optical density of medium ‘B’ is greater than the optical density of medium ‘A’ and medium ‘C’.$
Refraction of Light
35 $(a) Write the name of the lens and position of the object in front of it so that a virtual and magnified image is formed. (b) An object is placed perpendicular to the principal axis of a convex lens of focal length 20 cm. If object is located at 30 cm from this lens, using lens formula find out the position and nature of the image formed.$
Lens Formula and Power of a Lens
35 $(a) Write the expression for the magnification produced by a lens in terms of object distance and image distance. (b) A 4 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 20 cm. Calculate the size of the image formed, if the distance of the object from the lens is 10 cm.$
Lens Formula and Power of a Lens

Medium	Speed of light (m/s)
A	$2.25 \times 10^8$
B	$2 \times 10^8$
C	$2.08 \times 10^8$

Material Medium	Refractive Index
A	1.50
B	1.46
C	1.31
D	1.77

The variation of image distance

(v)

with the object distance

(u)

for a convex lens is given in the following observation table. Analyse it and answer the questions given below :

S.No.	Object distance $(u)$ cm	Image distance $(v)$ cm
1	$-150$	$+30$
2	$-75$	$+37{\cdot}5$
3	$-50$	$+50$
4	$-37{\cdot}5$	$+75$
5	$-30$	$+150$
6	$-15$	$+37{\cdot}5$

38 (a)

Without calculation, find out the focal length of the given convex lens. Justify your answer.

Lens Formula and Power of a Lens

36 $An object is placed at a distance of 30 cm in front of a convex lens of focal length 15 cm. Use lens formula to determine the position of the image. What will be the size of the image in this case ?$
Lens Formula and Power of a Lens
36 $An object of height 6 cm is placed at a distance of 30 cm from the optical centre of a concave lens of focal length 15 cm. Use lens formula to determine : (a) The distance of image from the optical centre. (b) The height of the image formed.$
Lens Formula and Power of a Lens

The variation of image distance

(v)

with the object distance

(u)

for a convex lens is given in the following observation table. Analyse it and answer the questions given below :

S.No.	Object distance $(u)$ cm	Image distance $(v)$ cm
1	$-150$	$+30$
2	$-75$	$+37{\cdot}5$
3	$-50$	$+50$
4	$-37{\cdot}5$	$+75$
5	$-30$	$+150$
6	$-15$	$+37{\cdot}5$

38 (b)

Which one of the observations given in the table is not correct and why ?

Lens Formula and Power of a Lens

36 $-2$
Spherical Mirrors and Image Formation
37 $A mirror used for rear-view of an automobile has a focal length 2.0 m. If a car is located at 8.0 m from the mirror - (a) Find out the position of the image of this car as seen in the mirror. (b) Draw the ray-diagram for image formation by the rear-view mirror.$
Mirror Formula and Magnification

The variation of image distance

(v)

with the object distance

(u)

for a convex lens is given in the following observation table. Analyse it and answer the questions given below :

S.No.	Object distance $(u)$ cm	Image distance $(v)$ cm
1	$-150$	$+30$
2	$-75$	$+37{\cdot}5$
3	$-50$	$+50$
4	$-37{\cdot}5$	$+75$
5	$-30$	$+150$
6	$-15$	$+37{\cdot}5$

38 (c) (i)

u = -30

Lens Formula and Power of a Lens

The above ray diagram is to show image formation by a reflecting telescope. Reflecting telescope revolutionized our way of looking into the sky. Reflecting telescopes employ large mirrors to gather and focus light rather than relying solely on lenses as we do in the refracting telescopes. These telescopes utilize precisely shaped and polished mirrors to capture incoming light and reflect it to a focal point, where the telescope forms an image for observation.
38 (a) $What kind of image of a star is seen by the observer in the eye-piece ?$
Spherical Mirrors and Image Formation

The variation of image distance

(v)

with the object distance

(u)

for a convex lens is given in the following observation table. Analyse it and answer the questions given below :

S.No.	Object distance $(u)$ cm	Image distance $(v)$ cm
1	$-150$	$+30$
2	$-75$	$+37{\cdot}5$
3	$-50$	$+50$
4	$-37{\cdot}5$	$+75$
5	$-30$	$+150$
6	$-15$	$+37{\cdot}5$

38 (c) (ii)

u = -30

Spherical Lenses and Image Formation

Lenses can form different types of images depending upon their focal length and position of object. A convex lens can create real, inverted or virtual, erect images, while a concave lens forms only virtual and diminished images. The focal length determines the power of lens. Convex lenses have positive focal length while concave lenses have negative focal length by convention. When lenses are placed together, their combined power is determined by the sum of their individual powers. Ray diagrams help to visualize how light converges or diverges through lens to form an image.
38 (a) $A convex lens of focal length 20 cm is used to form an image. If an object is placed at 40 cm from the lens, what will be the position and nature of image ?$
Spherical Lenses and Image Formation
The above ray diagram is to show image formation by a reflecting telescope. Reflecting telescope revolutionized our way of looking into the sky. Reflecting telescopes employ large mirrors to gather and focus light rather than relying solely on lenses as we do in the refracting telescopes. These telescopes utilize precisely shaped and polished mirrors to capture incoming light and reflect it to a focal point, where the telescope forms an image for observation.
38 (b) $What kind of mirror is used in this reflecting telescope ?$
Spherical Mirrors and Image Formation
Lenses can form different types of images depending upon their focal length and position of object. A convex lens can create real, inverted or virtual, erect images, while a concave lens forms only virtual and diminished images. The focal length determines the power of lens. Convex lenses have positive focal length while concave lenses have negative focal length by convention. When lenses are placed together, their combined power is determined by the sum of their individual powers. Ray diagrams help to visualize how light converges or diverges through lens to form an image.
38 (b) $Illustrate the formation of image with the help of ray diagram, when the object is placed between the optical centre and principal focus of concave lens.$
Spherical Lenses and Image Formation
The above ray diagram is to show image formation by a reflecting telescope. Reflecting telescope revolutionized our way of looking into the sky. Reflecting telescopes employ large mirrors to gather and focus light rather than relying solely on lenses as we do in the refracting telescopes. These telescopes utilize precisely shaped and polished mirrors to capture incoming light and reflect it to a focal point, where the telescope forms an image for observation.
38 (c) $Explain with the reason, what kind of optical device (type of lens or mirror) is used at the eye-piece.$
Spherical Lenses and Image Formation
Lenses can form different types of images depending upon their focal length and position of object. A convex lens can create real, inverted or virtual, erect images, while a concave lens forms only virtual and diminished images. The focal length determines the power of lens. Convex lenses have positive focal length while concave lenses have negative focal length by convention. When lenses are placed together, their combined power is determined by the sum of their individual powers. Ray diagrams help to visualize how light converges or diverges through lens to form an image.
38 (c) (i) $A lens combination consists of a convex lens of focal length 30 cm and a concave lens of focal length 15 cm placed together. Find the equivalent focal length and power of this lens combination.$
Lens Formula and Power of a Lens
Lenses can form different types of images depending upon their focal length and position of object. A convex lens can create real, inverted or virtual, erect images, while a concave lens forms only virtual and diminished images. The focal length determines the power of lens. Convex lenses have positive focal length while concave lenses have negative focal length by convention. When lenses are placed together, their combined power is determined by the sum of their individual powers. Ray diagrams help to visualize how light converges or diverges through lens to form an image.
38 (c) (ii) $Two lenses are placed in contact. One is a concave lens with focal length 2 m and the other is a convex lens with focal length 1.5 m. What type of lens will the combination behave as (convex or concave) ? Give reason.$
Lens Formula and Power of a Lens
The above ray diagram is to show image formation by a reflecting telescope. Reflecting telescope revolutionized our way of looking into the sky. Reflecting telescopes employ large mirrors to gather and focus light rather than relying solely on lenses as we do in the refracting telescopes. These telescopes utilize precisely shaped and polished mirrors to capture incoming light and reflect it to a focal point, where the telescope forms an image for observation.
38 (c) OR $What is the role of plane mirror in image formation by this telescope ?$
Reflection of Light

2025

33 q

10 $-1$
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Lens Formula and Power of a Lens
11 $An optical device ‘X’ is placed obliquely in the path of a narrow parallel beam of light. If the emergent beam gets displaced laterally, the device ‘X’ is :$
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Refraction of Light
11 $\dfrac{6}{5}$
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Refractive Index
11 $A candle flame is placed in front of the reflecting surface of a convex mirror of focal length f. If the distance of the flame from the pole of the mirror is ‘f’, its image is formed :$
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Mirror Formula and Magnification
11 $\frac{4}{3}$
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Refractive Index
12 $An object is placed at a distance of 30 cm from the pole of a concave mirror. If its real and inverted image is formed at 60 cm in front of the mirror, the focal length of the mirror is :$
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Mirror Formula and Magnification
13 $Identify from the following the ray diagram which shows the correct path of the reflected ray for the ray incident on a concave mirror as shown :$
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Spherical Mirrors and Image Formation
13 $Mirror ‘X’ is used to concentrate sunlight in solar furnace and Mirror ‘Y’ is fitted on the side of the vehicle to see the traffic behind the driver. Which of the following statements are true for the two mirrors ? (i) The image formed by mirror ‘X’ is real, diminished and at its focus. (ii) The image formed by mirror ‘Y’ is virtual, diminished and erect. (iii) The image formed by mirror ‘X’ is virtual, diminished and erect. (iv) The image formed by mirror ‘Y’ is real, diminished and at its focus.$
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Spherical Mirrors and Image Formation
13 $In order to obtain large images of the teeth of patients, the dentist holds the concave mirror in such a manner that the teeth are positioned$
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Spherical Mirrors and Image Formation
21 $During an experiment, a student observes that the given mirror is forming an erect and diminished image for all positions of the object placed in front of it. Based on the this information, answer the following questions : (a) Identify the mirror. (b) Using new Cartesian sign convention, write the magnitude of the magnification in this case. (c) What will be the radius of curvature of the mirror if its focal length is 20 cm ?$
Spherical Mirrors and Image Formation
21 $An object is placed at a distance of 10 cm in front of a concave mirror of focal length 15 cm. Use mirror formula to determine the position of the image formed by this mirror.$
Mirror Formula and Magnification
23 $When an incident ray of light enters a medium ‘X’ from air, it bends towards the normal. Infer about the following with respect to air : (a) Optical density of medium ‘X’. (b) Speed of light through medium ‘X’ Give reason for your answer in each case.$
Refractive Index
23 $An object is placed at a distance of 30 cm in front of a concave mirror of focal length 20 cm. Use mirror formula to determine the position of the image formed in this case.$
Mirror Formula and Magnification
24 $An object is placed at a distance of 60 cm from a concave lens of focal length 30 cm. Use lens formula to find the position of the image formed in this case.$
Lens Formula and Power of a Lens
24 $The values of absolute refractive indices of kerosene and water are 1.44 and 1.33 respectively. Compare the two media on the basis of their (a) optical density (b) mass density (c) relative speed of propagation of light. What do you infer on the basis of above comparisons ?$
Refractive Index
24 $Study the figure in which the path of a ray of light going from Medium 1 to Medium 2 is shown. (a) Out of the two Media – Medium 1 and Medium 2, in which is the speed of light more ? (b) State reason of bending of the refracted ray away from the normal. (c) Express refractive index of Medium 2 with respect to Medium 1 in terms of speed of light in two media.$
Refraction of Light
25 (a) $Out of the two lenses, one concave and the other convex, state which one will diverge a parallel beam of light falling on it. Draw a ray diagram to show the principal focus of the lens.$
Spherical Lenses and Image Formation
25 (b) $A ray of light after refraction from a convex lens emerges parallel to its principal axis. (i) Draw a labelled ray diagram to show it. (ii) In this case, the incident ray before refraction from the lens passes through a point on its principal axis. Name the point.$
Spherical Lenses and Image Formation
29 $An object of size 5 cm is placed at a distance of 30 cm from the optical centre of a converging lens of focal length 20 cm. Use lens formula to determine the position and size of the image formed.$
Lens Formula and Power of a Lens
31 $-2$
Mirror Formula and Magnification
31 $8{\cdot}0$
Lens Formula and Power of a Lens
31 $If we want to obtain a virtual and magnified image of an object by using a concave mirror of focal length 18 cm, where should the object be placed? Use mirror formula to determine the object distance for an image of magnification +2 produced by this mirror to justify your answer.$
Mirror Formula and Magnification

-90

S.No.	Distance of flame from the lens (cm)	Distance of the image from the lens
1	$-90$	$+18$
2	$-60$	$+20$
3	$-40$	$+24$
4	$-30$	$+30$
5	$-24$	$+40$
6	$-20$	$+60$
7	$-18$	$+90$
8	$-12$	$+120$

Spherical Lenses and Image Formation

31 $1{\cdot}5$
Mirror Formula and Magnification
31 $Draw ray diagrams to show the nature, position and relative size of the image formed by a convex mirror when the object is placed (i) at infinity and (ii) between infinity and pole P of the mirror.$
Spherical Mirrors and Image Formation
31 $-0.25$
Lens Formula and Power of a Lens
31 $An object is placed at a distance of 20 cm from the optical centre of a concave lens and its image is formed on the same side of the lens as the object. If the distance of the image from optical centre of the lens is 10 cm, use lens formula to determine (i) focal length, and (ii) power of the lens in new Cartesian sign conventions.$
Lens Formula and Power of a Lens
36 (a) $(a) Observe the following diagram and compare (i) speed of light and (ii) optical densities of the three media A, B and C. Also give justification for your answer of any one of the two cases in terms of refractive indices of A, B and C. (b) Redraw the path of a ray of light through the three media, if the ray of light starting from medium A falls on the medium B (i) Obliquely and the optical density of medium B is made more than that of A and C. (ii) The ray falls normally from medium A to medium B.$
Refraction of Light
36 (a) $(i) “In refraction of light through a rectangular glass slab, the emergent ray is always parallel to the direction of the incident ray.” Why ? Explain with the help of a ray diagram. What happens when a ray of light falls normally on one of the faces of a rectangular glass prism ? Draw diagram. (ii) An object is placed at a distance of 30 cm from the optical centre of a concave lens of focal length 20 cm. Use Lens formula to determine the position of the image formed in this case.$
Refraction of Light
36 (a) $-2{\cdot}5$
Lens Formula and Power of a Lens
36 (b) $(i) Draw a ray diagram to show the refraction of a ray of light through a rectangular glass slab when it falls obliquely from air into glass. (ii) State Snell’s law of refraction of light. (iii) Differentiate between the virtual images formed by a convex lens and a concave lens on the basis of : (I) object distance, and (II) magnification.$
Refraction of Light
36 (b) $3{\cdot}0$
Mirror Formula and Magnification

36 (b)

-15

Observation Number	Object distance (u) in cm	Image distance (v) in cm
1	$-15$	$-60$
2	$-25$	$+100$
3	$-30$	$+60$
4	$-40$	$+40$
5	$-60$	$+30$
6	$-100$	$+25$

Spherical Lenses and Image Formation

2024

28 q

11 $\frac{3}{2}$
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Refractive Index
11 $How will the image formed by a convex lens be affected, if the upper half of the lens is wrapped with a black paper ?$
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Spherical Lenses and Image Formation
12 $At what distance from a convex lens should an object be placed to get an image of the same size as that of the object on a screen ?$
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Spherical Lenses and Image Formation
15 $3 \times 10^8$
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Refractive Index
23 $\theta$
Refraction of Light
24 $An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position of the image formed by the mirror.$
Mirror Formula and Magnification
24 (a) $State two laws of refraction of light.$
Refraction of Light
24 (b) $3 \times 10^8$
Refractive Index
25 $+3$
Mirror Formula and Magnification
25 $Define power of a lens. Find power of a lens whose focal length is 50 cm.$
Lens Formula and Power of a Lens
25 $The heat produced at a point due to concentration of sunlight by a convex lens burns a paper. (a) Explain why it happens. (b) Name the term (in the context of the lens used) given to the point at which the paper starts burning. What does the bright spot formed on the paper represent ?$
Spherical Lenses and Image Formation
31 (a) $An object is placed in front of a concave mirror of focal length 12 cm. If distance of the object from the pole of the mirror is 8 cm, then use mirror formula to determine the position of the image formed. Draw a labelled ray diagram to justify your answer in this case.$
Mirror Formula and Magnification
31 (b) $(i) The image of an object formed by a mirror is real, inverted and is of magnification-1. If the image is at a distance of 30 cm from the mirror, where is the object placed ? Give reason to justify your answer. (ii) Where would the image be if the object is moved 15 cm towards the mirror ? Draw ray diagram for the new position of the object to justify your answer.$
Mirror Formula and Magnification

36 (a)

-150

Spherical Lenses and Image Formation

36 (a) $(i) Draw a ray diagram to show the path of the refracted ray in each of the following cases : A ray of light incident on a concave lens (1) parallel to its principal axis, and (2) is directed towards its principal focus. (ii) A 4 cm tall object is placed perpendicular to the principal axis of convex lens of focal length 24 cm. The distance of object from the lens is 16 cm. Find the position and size of image formed.$
Lens Formula and Power of a Lens
36 (a) $5{\cdot}0$
Mirror Formula and Magnification
36 (b) $(i) Define principal axis of a lens. Draw a ray diagram to show what happens when a ray of light parallel to the principal axis of a concave lens passes through it. (ii) The focal length of a concave lens is 20 cm. At what distance from the lens should a 5 cm tall object be placed so that its image is formed at a distance of 15 cm from the lens ? Also calculate the size of the image formed.$
Lens Formula and Power of a Lens
36 (b) $(i) Draw a ray diagram to show the path of the reflected ray in each of the following cases : A ray of light incident on a convex mirror (1) parallel to its principal axis, and (2) is directed towards its principal focus (ii) A 1.5 cm tall candle flame is placed perpendicular to the principal axis of a concave mirror of focal length 12 cm. If the distance of the flame from the pole of the mirror is 18 cm, use mirror formula to determine the position and size of the image formed.$
Mirror Formula and Magnification
36 $(a) Upper half of a convex lens is covered with a black paper. Draw a ray diagram to show the formation of image of an object placed at a distance of 2F from such a lens. Mention the position and nature of the image formed. State the observable difference in the image obtained if the lens is uncovered. Give reason to justify your answer. (b) An object is placed at a distance of 30 cm from the optical centre of a concave lens of focal length 15 cm. Use lens formula to determine the distance of the image from the optical centre of the lens.$
Spherical Lenses and Image Formation
36 (b) $(i) State laws of refraction of light. (ii) Draw a ray diagram to show refraction of a ray of light through a rectangular glass slab. How is the emergent ray related to incident ray ? Mark lateral displacement in the diagram.$
Refraction of Light
A highly polished surface such as a mirror reflects most of the light falling on it. In our daily life we use two types of mirrors — plane and spherical. The reflecting surface of a spherical mirrors may be curved inwards or outwards. In concave mirrors, reflection takes place from the inner surface, while in convex mirrors reflection takes place from the outer surface.
39 (a) $Define the principal axis of a concave mirror.$
Spherical Mirrors and Image Formation
Study the data given below showing the focal length of three concave mirrors A, B and C and the respective distances of objects placed in front of the mirrors :
Case Mirror Focal Length (cm) Object Distance (cm)
1 A 20 45
2 B 15 30
3 C 30 20
39 (i) $In which one of the above cases the mirror will form a diminished image of the object ? Justify your answer.$
Spherical Mirrors and Image Formation
A highly polished surface such as a mirror reflects most of the light falling on it. In our daily life we use two types of mirrors — plane and spherical. The reflecting surface of a spherical mirrors may be curved inwards or outwards. In concave mirrors, reflection takes place from the inner surface, while in convex mirrors reflection takes place from the outer surface.
39 (b) $A ray of light is incident on a concave mirror, parallel to its principal axis. If this ray after reflection from the mirror passes through the principal axis from a point at a distance of 10 cm from the pole of the mirror, find the radius of curvature of the mirror.$
Spherical Mirrors and Image Formation
Study the data given below showing the focal length of three concave mirrors A, B and C and the respective distances of objects placed in front of the mirrors :
Case Mirror Focal Length (cm) Object Distance (cm)
1 A 20 45
2 B 15 30
3 C 30 20
39 (ii) $List two properties of the image formed in case 2.$
Spherical Mirrors and Image Formation
A highly polished surface such as a mirror reflects most of the light falling on it. In our daily life we use two types of mirrors — plane and spherical. The reflecting surface of a spherical mirrors may be curved inwards or outwards. In concave mirrors, reflection takes place from the inner surface, while in convex mirrors reflection takes place from the outer surface.
39 (c) (i) $An object is placed at a distance of 10 cm from the pole of a convex mirror of focal length 15 cm. Find the position of the image.$
Mirror Formula and Magnification
Study the data given below showing the focal length of three concave mirrors A, B and C and the respective distances of objects placed in front of the mirrors :
Case Mirror Focal Length (cm) Object Distance (cm)
1 A 20 45
2 B 15 30
3 C 30 20
39 (iii) (A) $What is the nature and size of the image formed by mirror C ? Draw ray diagram to justify your answer.$
Spherical Mirrors and Image Formation
A highly polished surface such as a mirror reflects most of the light falling on it. In our daily life we use two types of mirrors — plane and spherical. The reflecting surface of a spherical mirrors may be curved inwards or outwards. In concave mirrors, reflection takes place from the inner surface, while in convex mirrors reflection takes place from the outer surface.
39 (c) (ii) $A mirror forms a virtual, erect and diminished image of an object. Identify the type of this mirror. Draw a ray diagram to show the image formation in this case.$
Spherical Mirrors and Image Formation
Study the data given below showing the focal length of three concave mirrors A, B and C and the respective distances of objects placed in front of the mirrors :
Case Mirror Focal Length (cm) Object Distance (cm)
1 A 20 45
2 B 15 30
3 C 30 20
39 (iii) (B) $An object is placed at a distance of 18 cm from the pole of a concave mirror of focal length 12 cm. Find the position of the image formed in this case.$
Mirror Formula and Magnification

Case	Mirror	Focal Length (cm)	Object Distance (cm)
1	A	20	45
2	B	15	30
3	C	30	20

Case	Mirror	Focal Length (cm)	Object Distance (cm)
1	A	20	45
2	B	15	30
3	C	30	20

Case	Mirror	Focal Length (cm)	Object Distance (cm)
1	A	20	45
2	B	15	30
3	C	30	20

Case	Mirror	Focal Length (cm)	Object Distance (cm)
1	A	20	45
2	B	15	30
3	C	30	20

2023

38 q

7 $In torch lights and head lights of vehicles, the bulb is placed$
Tap an option to check your answer.
Spherical Mirrors and Image Formation
7 $A student wants to obtain an erect image of an object using a concave mirror of 10 cm focal length. What will be the distance of the object from mirror ?$
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Spherical Mirrors and Image Formation
7 $To obtain a magnification of + 2 with a concave mirror of radius of curvature 60 cm the object distance must be$
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Mirror Formula and Magnification
13 $An object is placed in front of a convex mirror at infinity. According to the New Cartesian Sign Convention, the sign of the focal length and the sign of the image distance in this case are respectively :$
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Mirror Formula and Magnification
25 $v_a$
Refractive Index
25 OR $(a) A ray of light starting from diamond is incident on the interface separating diamond and water. Draw a labelled ray diagram to show the refraction of light in this case. (b) Absolute refractive indices of diamond and water are 2.42 and 1.33 respectively. Find the value of refractive index of water w.r.t. diamond.$
Refractive Index
29 $+1/2$
Mirror Formula and Magnification
29 $A student wants to project the image of a candle flame on a screen 60 cm in front of a mirror by keeping the candle at a distance of 15 cm from its pole. (a) Name the type of mirror used. (b) Also calculate : (i) Magnification of the image produced (ii) Distance between object and its image (c) Draw a ray diagram to show the image formation.$
Mirror Formula and Magnification
30 (a) $(i) An object of 5 cm height is placed at a distance of 20 cm from the optical centre of a concave lens of focal length 18 cm. Calculate (1) image distance and (2) the magnification in this case. (ii) Compare the values of magnification obtained by a concave lens and a convex lens when both the lenses form virtual images.$
Lens Formula and Power of a Lens
30 (A) $An object is kept at a distance of 1m from a lens of power +2D : (i) Identify the type of lens. (ii) Calculate its focal length and distance of the image formed.$
Lens Formula and Power of a Lens
30 (b) $A convex lens can form a (i) real, inverted and magnified image as well as (ii) virtual, erect and magnified image of an object. If the focal length of the lens is 10 cm, what should be the range of the object distance in both cases ? Draw ray diagrams to justify your answer.$
Spherical Lenses and Image Formation
31 (a) $A student has focussed the image of an object of height 3 cm on a white screen using a concave mirror of focal length 12 cm. If the distance of the object from the mirror is 18 cm, find the values of the following : (i) Distance of the image from the mirror (ii) Height of the image$
Mirror Formula and Magnification
30 (A) $Define the following terms in the context of a diverging mirror : (i) Principal focus (ii) Focal length Draw a labelled ray diagram to illustrate your answer.$
Spherical Mirrors and Image Formation
30 $(a) Complete the following ray diagram to show the formation of image : (b) Mention the nature, position and size of the image formed in this case. (c) State the sign of the image distance in this case using the Cartesian sign convention.$
Spherical Mirrors and Image Formation
30 $(a) The image of an object formed by a lens is of same size but inverted. If the object distance is 30 cm, calculate (i) The distance between the object and its image. (ii) Focal length of the lens. (b) Draw a ray diagram to show the image formed in above case.$
Spherical Lenses and Image Formation
30 (B) $Define the following terms in the context of a diverging lens : (i) Principal focus, (ii) Focal length. Draw a labelled ray diagram to illustrate your answer.$
Spherical Lenses and Image Formation
31 (b) $-10$
Lens Formula and Power of a Lens
30 (B) $An object of height 10 cm is placed 25 cm away from the optical centre of a converging lens of focal length 15 cm. Calculate the image-distance and height of the image formed.$
Lens Formula and Power of a Lens
31 $The power of a lens is +4D. Find the focal length of this lens. An object is placed at a distance of 50 cm from the optical centre of this lens. State the nature and magnification of the image formed by the lens and also draw a ray diagram to justify your answer.$
Lens Formula and Power of a Lens
36 $(a) Name the type of mirror that should be used to obtain the following types of images : (i) A magnified and virtual image of an object (ii) A diminished and virtual image of an object (b) Draw labelled ray diagrams to justify your answers in each case mentioned above. (c) Which of these mirrors can also be used to obtain a magnified and real image of an object ? State the position of the object in this case.$
Spherical Mirrors and Image Formation
36 $(a) Draw a ray diagram for showing the convergence of a parallel beam of light by a concave mirror and mark the positions of pole and the centre of curvature in it. (b) An object 4 cm in size is placed at 25 cm in front of a concave mirror of focal length 15 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image ? Find the nature and size of the image. (c) List any two uses of a concave mirror.$
Mirror Formula and Magnification
36 $(a) An object is placed in front of a convex lens of focal length f. If the distance of the object from the lens is 2f, draw a ray diagram to show the formation of the image. Write the value of magnification in this case. (b) A student has focussed the image of a candle flame on a white screen using a convex lens. The situation is as given below : Length of the flame = 2 cm Focal length of the lens = 12 cm Distance of the flame from the lens = 16 cm If the flame is perpendicular to the principal axis of the lens, calculate the values of the following : (i) Distance of the image from the lens (ii) Length of the image formed$
Lens Formula and Power of a Lens
A student took three concave mirrors of different focal lengths and performed the experiment to see the image formation by placing an object at different distances with these mirrors as shown in the following table.
Case No. Object-distance Focal length
I 45 cm 20 cm
II 30 cm 15 cm
III 20 cm 30 cm
39 (a) $List two properties of the image formed in Case I.$
Spherical Mirrors and Image Formation
Many optical instruments consist of a number of lenses. They are combined to increase the magnification and sharpness of the image. The net power (P) of the lenses placed in contact is given by the algebraic sum of the powers of the individual lenses $\mathrm{P_1, P_2, P_3 \ldots}$ as $\mathrm{P = P_1 + P_2 + P_3 \ldots}$ This is also termed as the simple additive property of the power of lens, widely used to design lens systems of cameras, microscopes and telescopes. These lens systems can have a combination of convex lenses and also concave lenses.
39 (a) $+4$
Lens Formula and Power of a Lens
Hold a concave mirror in your hand and direct its reflecting surface towards the sun. Direct the light reflected by the mirror on to a white card-board held close to the mirror. Move the card-board back and forth gradually until you find a bright, sharp spot of light on the board. This spot of light is the image of the sun on the sheet of paper; which is also termed as “Principal Focus” of the concave mirror.
39 (a) $List two applications of concave mirror.$
Spherical Mirrors and Image Formation
A student took three concave mirrors of different focal lengths and performed the experiment to see the image formation by placing an object at different distances with these mirrors as shown in the following table.
Case No. Object-distance Focal length
I 45 cm 20 cm
II 30 cm 15 cm
III 20 cm 30 cm
39 (b) $In which one of the cases given in the table, the mirror will form real image of same size and why ?$
Spherical Mirrors and Image Formation
The ability of a medium to refract light is expressed in terms of its optical density. Optical density has a definite connotation. It is not the same as mass density. On comparing two media, the one with the large refractive index is optically denser medium than the other. The other medium with a lower refractive index is optically rarer. Also the speed of light through a given medium is inversely proportional to its optical density.
39 (i) $3 \times 10^{8}$
Refractive Index
Many optical instruments consist of a number of lenses. They are combined to increase the magnification and sharpness of the image. The net power (P) of the lenses placed in contact is given by the algebraic sum of the powers of the individual lenses $\mathrm{P_1, P_2, P_3 \ldots}$ as $\mathrm{P = P_1 + P_2 + P_3 \ldots}$ This is also termed as the simple additive property of the power of lens, widely used to design lens systems of cameras, microscopes and telescopes. These lens systems can have a combination of convex lenses and also concave lenses.
39 (b) $-2{\cdot}5$
Lens Formula and Power of a Lens
Many optical instruments consist of a number of lenses. They are combined to increase the magnification and sharpness of the image. The net power (P) of the lenses placed in contact is given by the algebraic sum of the powers of the individual lenses $\mathrm{P_1, P_2, P_3 \ldots}$ as $\mathrm{P = P_1 + P_2 + P_3 \ldots}$ This is also termed as the simple additive property of the power of lens, widely used to design lens systems of cameras, microscopes and telescopes. These lens systems can have a combination of convex lenses and also concave lenses.
39 (c) $+0{\cdot}1$
Spherical Lenses and Image Formation
Hold a concave mirror in your hand and direct its reflecting surface towards the sun. Direct the light reflected by the mirror on to a white card-board held close to the mirror. Move the card-board back and forth gradually until you find a bright, sharp spot of light on the board. This spot of light is the image of the sun on the sheet of paper; which is also termed as “Principal Focus” of the concave mirror.
39 (b) $If the distance between the mirror and the principal focus is 15 cm, find the radius of curvature of the mirror.$
Spherical Mirrors and Image Formation
A student took three concave mirrors of different focal lengths and performed the experiment to see the image formation by placing an object at different distances with these mirrors as shown in the following table.
Case No. Object-distance Focal length
I 45 cm 20 cm
II 30 cm 15 cm
III 20 cm 30 cm
39 (c) $Name the type of mirror used by dentists. Give reason why do they use such type of mirrors.$
Spherical Mirrors and Image Formation
The ability of a medium to refract light is expressed in terms of its optical density. Optical density has a definite connotation. It is not the same as mass density. On comparing two media, the one with the large refractive index is optically denser medium than the other. The other medium with a lower refractive index is optically rarer. Also the speed of light through a given medium is inversely proportional to its optical density.
39 (ii) $\theta$
Refractive Index
A student took three concave mirrors of different focal lengths and performed the experiment to see the image formation by placing an object at different distances with these mirrors as shown in the following table.
Case No. Object-distance Focal length
I 45 cm 20 cm
II 30 cm 15 cm
III 20 cm 30 cm
39 (c) OR $Look at the table and identify the situation (object distance and focal length) which resembles the situation in which concave mirrors are used as shaving mirrors ? Draw a ray diagram to show the image formation in this case.$
Spherical Mirrors and Image Formation
Hold a concave mirror in your hand and direct its reflecting surface towards the sun. Direct the light reflected by the mirror on to a white card-board held close to the mirror. Move the card-board back and forth gradually until you find a bright, sharp spot of light on the board. This spot of light is the image of the sun on the sheet of paper; which is also termed as “Principal Focus” of the concave mirror.
39 (c) $Draw a ray diagram to show the type of image formed when an object is placed between pole and focus of a concave mirror.$
Spherical Mirrors and Image Formation
The ability of a medium to refract light is expressed in terms of its optical density. Optical density has a definite connotation. It is not the same as mass density. On comparing two media, the one with the large refractive index is optically denser medium than the other. The other medium with a lower refractive index is optically rarer. Also the speed of light through a given medium is inversely proportional to its optical density.
39 (iii) (A) $2 \times 10^{8}$
Refractive Index
Many optical instruments consist of a number of lenses. They are combined to increase the magnification and sharpness of the image. The net power (P) of the lenses placed in contact is given by the algebraic sum of the powers of the individual lenses $\mathrm{P_1, P_2, P_3 \ldots}$ as $\mathrm{P = P_1 + P_2 + P_3 \ldots}$ This is also termed as the simple additive property of the power of lens, widely used to design lens systems of cameras, microscopes and telescopes. These lens systems can have a combination of convex lenses and also concave lenses.
39 (c) OR $How is a virtual image formed by a convex lens different from that formed by a concave lens ? Under what conditions do a convex and a concave lens form virtual images ?$
Spherical Lenses and Image Formation
Hold a concave mirror in your hand and direct its reflecting surface towards the sun. Direct the light reflected by the mirror on to a white card-board held close to the mirror. Move the card-board back and forth gradually until you find a bright, sharp spot of light on the board. This spot of light is the image of the sun on the sheet of paper; which is also termed as “Principal Focus” of the concave mirror.
39 (c) OR $An object 10 cm in size is placed at 100 cm in front of a concave mirror. If its image is formed at the same point where the object is located, find : (i) focal length of the mirror, and (ii) magnification of the image formed with sign as per Cartesian sign convention.$
Mirror Formula and Magnification
The ability of a medium to refract light is expressed in terms of its optical density. Optical density has a definite connotation. It is not the same as mass density. On comparing two media, the one with the large refractive index is optically denser medium than the other. The other medium with a lower refractive index is optically rarer. Also the speed of light through a given medium is inversely proportional to its optical density.
39 (iii) (B) $4/3$
Refractive Index

Case No.	Object-distance	Focal length
I	45 cm	20 cm
II	30 cm	15 cm
III	20 cm	30 cm

Case No.	Object-distance	Focal length
I	45 cm	20 cm
II	30 cm	15 cm
III	20 cm	30 cm

Case No.	Object-distance	Focal length
I	45 cm	20 cm
II	30 cm	15 cm
III	20 cm	30 cm

Case No.	Object-distance	Focal length
I	45 cm	20 cm
II	30 cm	15 cm
III	20 cm	30 cm

The 10 board questions to practise first

The questions and kinds of question the board asked most often come first. Each one says how often and when.

Question 1
This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026 See all 4 of this type
36 $An object of height 6 cm is placed at a distance of 30 cm from the optical centre of a concave lens of focal length 15 cm. Use lens formula to determine : (a) The distance of image from the optical centre. (b) The height of the image formed.$
Question 2
This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026 See all 4 of this type
30 $Rays from the sun converge at a point 25 cm behind a convex lens. The distance at which an object be placed in front of the lens to get a virtual image, is :$
Tap an option to check your answer.
Question 3
This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026 See all 4 of this type
33 $2.25 \times 10^8$
Question 4
Asked 3 times: 2024*, 2025*, 2026 (* = numbers or wording changed that year) See all 3 times it was asked
33 $Draw the ray diagram showing refraction through a glass slab and write the relation between angle of incidence, angle of refraction and refractive index of glass.$

Medium	Speed of light (m/s)
A	$2.25 \times 10^8$
B	$2 \times 10^8$
C	$2.08 \times 10^8$

Question 5 (case study, 4 parts)

Asked 3 times: 2024*, 2025*, 2026 (* = numbers or wording changed that year) See all 3 times it was asked

The variation of image distance

(v)

with the object distance

(u)

for a convex lens is given in the following observation table. Analyse it and answer the questions given below :

S.No.	Object distance $(u)$ cm	Image distance $(v)$ cm
1	$-150$	$+30$
2	$-75$	$+37{\cdot}5$
3	$-50$	$+50$
4	$-37{\cdot}5$	$+75$
5	$-30$	$+150$
6	$-15$	$+37{\cdot}5$

38 (a)

Without calculation, find out the focal length of the given convex lens. Justify your answer.

38 (b)

Which one of the observations given in the table is not correct and why ?

38 (c) (i)

u = -30

38 (c) (ii)

u = -30

Question 6
Asked 3 times: 2023*, 2024*, 2026 (* = numbers or wording changed that year) See all 3 times it was asked
30 $A convex lens of focal length 15 cm, is forming a real image. If the size of image is same as the size of object, then position of object and position of image will be, respectively :$
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Question 7
This type asked 3 times: 2023, 2025, 2026. This one: 2026 See all 3 of this type
35 $(a) Write the expression for the magnification produced by a lens in terms of object distance and image distance. (b) A 4 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 20 cm. Calculate the size of the image formed, if the distance of the object from the lens is 10 cm.$
Question 8
This type asked 3 times: 2023, 2024, 2026. This one: 2026 See all 3 of this type
30 $From the following options choose the one which gives negative magnification greater than one :$
Tap an option to check your answer.
Question 9
This type asked 3 times: 2023, 2025, 2026. This one: 2026 See all 3 of this type
34 $Redraw the following ray diagrams in your answer book and show the path of reflected/refracted ray :$
Question 10
This type asked 3 times: 2024, 2025, 2026. This one: 2026 See all 3 of this type
35 $(a) State the laws which help to find out the angle of incidence and angle of reflection in the ray diagram given above. (b) Find out the angle of incidence and angle of reflection in the given ray diagram.$

Quick revision

7 most-asked questions · 14 key points · 9 formulas · 6 diagrams

Checked against NCERT Science (CBSE Class 10), Chapter 9.

Most asked in board papers

1
Mirrors: ray diagrams, nature of the image for each object position, uses (dentist, shaving, headlights, rear-view, solar furnace), definitions
Asked 4 times: 2026, 2025, 2024, 2023 · 1 mark
2
Lens numericals and u-v tables: lens formula, magnification, image of the same size at 2F, finding f from data
Asked 4 times: 2026, 2025, 2024, 2023 · 3 marks
3
Refractive index: absolute and relative, speed of light, optical density, bending towards or away from the normal
Asked 4 times: 2026, 2025, 2024, 2023 · 2 marks
4
Mirror numericals: mirror formula and magnification (concave mirror, rear-view convex mirror), $R = 2f$
Asked 4 times: 2026, 2025, 2024, 2023
5
Lens ray diagrams: image for each object position, half-covered lens, virtual image by convex and concave lens
Asked 4 times: 2026, 2025, 2024, 2023 · 2 marks
6
Power of a lens in dioptres, its sign, and lenses in contact
Asked 4 times: 2026, 2025, 2024, 2023
7
Laws of reflection and refraction; refraction through a rectangular glass slab
Asked 3 times: 2026, 2025, 2024

Must-know points

Laws of reflection: (i) The angle of incidence is equal to the angle of reflection. (ii) The incident ray, the normal to the mirror at the point of incidence and the reflected ray all lie in the same plane. They hold for all reflecting surfaces, curved ones too. A plane mirror's image is virtual, erect, same size and laterally inverted.
Spherical mirror terms: Pole P: centre of the mirror's surface. Centre of curvature C, radius of curvature R. Principal axis: the line through P and C, normal to the mirror at P. Principal focus F: where rays parallel to the axis meet (concave) or appear to come from (convex). Focal length f = PF. For small apertures $R = 2f$ .
Rules for ray diagrams: (i) A ray parallel to the axis passes through F after reflection (concave) or appears to come from F (convex). (ii) A ray through F (or aimed at F) comes out parallel. (iii) A ray through C (or aimed at C) returns along itself. (iv) A ray at P reflects at an equal angle. For lenses, a ray through the optical centre goes straight.
Images by a concave mirror: Object at infinity: image at F, point-sized. Beyond C: between F and C, diminished. At C: at C, same size. Between C and F: beyond C, enlarged. At F: at infinity. In all these it is real and inverted. Between P and F: behind the mirror, virtual, erect, enlarged.
Convex mirror: Always forms a virtual, erect and diminished image, between P and F behind the mirror (for the object at infinity, a point at F). Used as rear-view (wing) mirrors: the image is erect and they have a wider field of view as they curve outwards.
Uses of concave mirrors: Torches, search-lights and vehicle headlights (bulb at F, for a parallel beam); shaving mirrors and dentists' mirrors (object between P and F, enlarged erect image); solar furnaces (concentrate sunlight to heat).
New Cartesian Sign Convention: The object is on the left. All distances are measured from the pole (optical centre for a lens). Distances in the direction of incident light (right) are positive; against it (left) negative. Heights above the axis positive, below negative. So u is always negative; a concave mirror has f negative, a convex mirror f positive.
Magnification: Ratio of image height to object height. Negative m: real, inverted image; positive m: virtual, erect. $|m| > 1$ enlarged, $|m| = 1$ same size, $|m| < 1$ diminished. A convex mirror and a concave lens always give m between 0 and +1.
Laws of refraction: (i) The incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane. (ii) The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for light of a given colour and a given pair of media (Snell's law).
Refractive index and optical density: Absolute refractive index: speed of light in vacuum divided by speed in the medium. The medium with the larger refractive index is optically denser. Light going from rarer to denser slows down and bends towards the normal; denser to rarer, it speeds up and bends away. Kerosene (1.44) is optically denser than water (1.33) though lighter.
Glass slab: Light bends towards the normal entering the glass and away from it leaving. The emergent ray is parallel to the incident ray, shifted sideways (lateral displacement), because the bending at the two parallel faces is equal and opposite. A ray falling normally goes straight through.
Images by a convex lens: Object at infinity: at $F_2$ , point-sized. Beyond $2F_1$ : between $F_2$ and $2F_2$ , diminished. At $2F_1$ : at $2F_2$ , same size. Between $F_1$ and $2F_1$ : beyond $2F_2$ , enlarged. At $F_1$ : at infinity. These are real and inverted. Between $F_1$ and O: same side, virtual, erect, enlarged.
Concave lens: Diverges a parallel beam; always gives a virtual, erect and diminished image on the same side as the object, between the optical centre and F (at F for an object at infinity). A convex lens converges light.
Power of a lens: The degree of convergence or divergence a lens produces: $P = \frac{1}{f}$ with f in metres. SI unit dioptre (D): 1 D is the power of a lens of focal length 1 m. Convex lens: positive power; concave lens: negative. For lenses in contact the powers add.

Formulas

Radius of curvature

R = 2f

Mirror formula

\frac{1}{v} + \frac{1}{u} = \frac{1}{f}

$f$ negative for a concave mirror, positive for a convex mirror

Magnification by a mirror

m = \frac{h'}{h} = -\frac{v}{u}

Lens formula

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

$f$ positive for a convex lens, negative for a concave lens

Magnification by a lens

m = \frac{h'}{h} = \frac{v}{u}

Snell's law

\frac{\sin i}{\sin r} = \text{constant} = n_{21}

Refractive index and speed

\begin{gathered}n_m = \frac{c}{v} \\ n_{21} = \frac{v_1}{v_2} = \frac{n_2}{n_1} \\ n_{12} = \frac{1}{n_{21}}\end{gathered}

Power of a lens

\begin{gathered}P = \frac{1}{f\,(\text{in m})} \\ 1\text{ D} = 1\text{ m}^{-1}\end{gathered}

Lenses in contact

P = P_1 + P_2 + P_3 + \ldots

Diagrams to practise

Image formation by a concave mirror (Figure 9.7): label P, F, C on the principal axis · two rays from the object top · image position for each object position · real images in front, virtual one behind
Image formation by a convex mirror (Figure 9.8): label ray parallel to axis, diverging as if from F · ray aimed at C returning back · dotted extensions behind the mirror · virtual, erect, diminished image between P and F
Image formation by a convex lens (Figure 9.16): label O, F₁, 2F₁, F₂, 2F₂ marked · ray parallel to axis through F₂ · ray through O undeviated · image for each object position
Image formation by a concave lens (Figure 9.17): label ray parallel to axis diverging as if from F₁ · ray through O undeviated · dotted extensions · virtual, erect, diminished image between F₁ and O
Refraction through a rectangular glass slab (Figure 9.10): label incident ray, normal, angle i · refracted ray bending towards the normal · emergent ray parallel to incident ray · lateral displacement
New Cartesian Sign Convention (Figure 9.9): label mirror at the origin, pole P · direction of incident light: + · distances against it: − · heights up +, down −

Mistakes that cost marks

Using the wrong sign for f or u

u is always negative (object on the left). Concave mirror:

f < 0

; convex mirror:

f > 0

. Convex lens:

f > 0

; concave lens:

f < 0

. A rear-view mirror with f = 1.5 m is a convex mirror, so use

f = +1.5

Mixing the mirror and lens formulas

Mirror:

\frac{1}{v} + \frac{1}{u} = \frac{1}{f}

m = -\frac{v}{u}

. Lens:

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

m = \frac{v}{u}

. Check: a real image from a concave mirror has v negative; from a convex lens v positive.

Power with f in centimetres

Change f to metres first: f = 50 cm gives P = 1/0.5 = +2 D. P = -2.5 D gives f = -0.4 m = -40 cm, a concave lens. Combination: +4 D and -2 D give +2 D, converging.

Relative refractive index upside down

n_{21}

(medium 2 with respect to 1) =

\frac{n_2}{n_1} = \frac{v_1}{v_2}

. Water to glass:

\frac{3/2}{4/3} = \frac{9}{8}

. Glass to water is

\frac{8}{9}

. Speed of light in a medium:

v = \frac{c}{n}

Half-covered lens

Covering half of a lens still gives the full image, only less bright, because every part of the lens forms the whole image.

Ray diagrams without arrows

Put arrows on every ray, draw virtual rays dotted, mark F and 2F (or C), and label the image with its nature: real or virtual, inverted or erect, size.

9.2 Spherical Mirrors

Questions

9.2.4 Mirror Formula and Magnification

Solved Examples

Questions

9.3 Refraction of Light

Questions

9.3.7-9.3.8 Lens Formula, Magnification and Power of a Lens

Solved Examples

Questions

Exercises

What the board has asked from this chapter

2026

2025

2024

2023

The 10 board questions to practise first

Question 1

Question 2

Question 3

Question 4

Question 5 (case study, 4 parts)

Question 6

Question 7

Question 8

Question 9

Question 10

Most asked in board papers

Must-know points

Formulas

Diagrams to practise

Mistakes that cost marks