Physics · Textbook solutions

Optics

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 65 questions

9. Optics — worked examples

14 q

Solved Examples

Worked · 14
  1. Solved Ex.9.1
    Thickness of the glass of a spectacle is 2 mm and refractive index of its glass is 1.5. Calculate time taken by light to cross this thickness. Express your answer with the most convenient prefix attached to the unit 'second'.
  2. Solved Ex.9.2
    A small object is kept symmetrically between two plane mirrors inclined at 38∘38^\circ. This angle is now gradually increased to 41∘41^\circ, the object being symmetrical all the time. Determine the number of images visible during the process.
  3. Solved Ex.9.3
    A thin pencil of length 20 cm is kept along the principal axis of a concave mirror of curvature 30 cm. Nearest end of the pencil is 20 cm from the pole of the mirror. What will be the size of image of the pencil?
  4. Solved Ex.9.4
    A crane flying 6 m above a still, clear water lake sees a fish underwater. For the crane, the fish appears to be 6 cm below the water surface. How much deep should the crane immerse its beak to pick that fish? For the fish, how much above the water surface does the crane appear? Refractive index of water = 4/3.
  5. Solved Ex.9.5
    There is a tiny LED bulb at the center of the bottom of a cylindrical vessel of diameter 6 cm. Height of the vessel is 4 cm. The beaker is filled completely with an optically dense liquid. The bulb is visible from any inclined position but just visible if seen along the edge of the beaker. Determine refractive index of the liquid.
  6. Solved Ex.9.6
    A glass paper-weight (n=1.5)(n = 1.5) of radius 3 cm has a tiny air bubble trapped inside it. Closest distance of the bubble from the surface is 2 cm. Where will it appear when seen from the other end (from where it is farthest)?
  7. Solved Ex.9.7
    A dense glass double convex lens (n=2)(n = 2) designed to reduce spherical aberration has ∣R1∣:∣R2∣=1:5|R_{1}| : |R_{2}| = 1 : 5. If a point object is kept 15 cm in front of this lens, it produces its real image at 7.5 cm. Determine R1R_{1} and R2R_{2}.
  8. Solved Ex.9.8
    A fine beam of white light is incident upon the longer side of a plane parallel glass slab of breadth 5 cm at angle of incidence 60060^{0}. Calculate angular deviation of red and violet rays within the slab and lateral dispersion between them as they emerge from the opposite side. Refractive indices of the glass for red and violet are 1.51 and 1.53 respectively.
  9. Solved Ex.9.9
    For a glass (n=1.5)(n = 1.5) prism having refracting angle 60060^{0}, determine the range of angle of incidence for which emergent ray is possible from the opposite surface and the corresponding angles of emergence. Also calculate the angle of incidence for which i=ei = e. How much is the corresponding angle of minimum deviation?
  10. Solved Ex.9.10
    For a dense flint glass prism of refracting angle 10010^{0}, obtain angular deviation for extreme colours and dispersive power of dense flint glass. (nred=1.712, nviolet=1.792)(n_{red} = 1.712,\ n_{violet} = 1.792)
  11. Solved Ex.9.11
    After Cataract operation, a person is recommended with concavo-convex spectacles of curvatures 10 cm and 50 cm. Crown glass of refractive indices 1.51 for red and 1.53 for violet colours is used for this. Calculate the lateral chromatic aberration occurring due to these glasses.
  12. Solved Ex.9.12
    A magnifying glass of focal length 10 cm is used to read letters of thickness 0.5 mm held 8 cm away from the lens. Calculate the image size. How big will the letters appear? Can you read the letters if held 5 cm away from the lens? If yes, of what size would the letters appear? If no, why not?
  13. Solved Ex.9.13
    The pocket microscope used by a student consists of eye lens of focal length 6.25 cm and objective of focal length 2 cm. At microscope length 15 cm, the final image appears biggest. Estimate distance of the object from the objective and magnifying power of the microscope.
  14. Solved Ex.9.14
    Focal length of the objective of an astronomical telescope is 1 m. Under normal adjustment, length of the telescope is 1.05 m. Calculate focal length of the eyepiece and magnifying power under normal adjustment.

Exercises

51 q

Choose the correct option

Practice · 13
  1. 1. Choose the correct option.
    Ex Q.1 (i)
    As per recent understanding *light* consists of
    1. A.
      rays
    2. B.
      waves
    3. C.
      corpuscles
    4. D.
      photons obeying the rules of waves
  2. Ex Q.1 (ii)
    Consider optically denser lenses P, Q, R and S drawn below. According to Cartesian sign convention which of these have positive focal length? [Figure: four lens cross-sections, drawn with light incident from the left. P is bounded by two arcs that both bulge towards the left and meet at sharp tips at the top and the bottom, the left-hand arc being far more strongly curved than the right-hand one. Q is the mirror image of P about a vertical line: both of its arcs bulge towards the right, the right-hand arc being the more strongly curved. R has short flat top and bottom edges; its left boundary is an arc bulging towards the left, while its right boundary is an arc that curves leftwards, in towards the body of the lens. S is the mirror image of R about a vertical line.]
    1. A.
      Only P
    2. B.
      Only P and Q
    3. C.
      Only P and R
    4. D.
      Only Q and S
  3. Ex Q.1 (iii)
    Two plane mirrors are inclined at angle 40040^{0} between them. Number of images seen of a tiny object kept between them is
    1. A.
      Only 8
    2. B.
      Only 9
    3. C.
      8 or 9
    4. D.
      9 or 10
  4. Ex Q.1 (iv)
    A concave mirror of curvature 40 cm, used for *shaving purpose* produces image of double size as that of the object. Object distance must be
    1. A.
      10 cm only
    2. B.
      20 cm only
    3. C.
      30 cm only
    4. D.
      10 cm or 30 cm
  5. Ex Q.1 (v)
    Which of the following aberrations will NOT occur for spherical mirrors?
    1. A.
      Chromatic aberration
    2. B.
      Coma
    3. C.
      Distortion
    4. D.
      Spherical aberration
  6. Ex Q.1 (vi)
    There are different fish, monkeys and water on the habitable planet of the star Proxima b. A fish swimming underwater feels that there is a monkey at 2.5 m on the top of a tree. The same monkey feels that the fish is 1.6 m below the water surface. Interestingly, height of the tree and the depth at which the fish is swimming are exactly same. Refractive index of that water must be
    1. A.
      6/5
    2. B.
      5/4
    3. C.
      4/3
    4. D.
      7/5
  7. Ex Q.1 (vii)
    Consider following phenomena/applications: P) Mirage, Q) rainbow, R) Optical fibre and S) glittering of a diamond. Total internal reflection is involved in
    1. A.
      Only R and S
    2. B.
      Only R
    3. C.
      Only P, R and S
    4. D.
      all the four
  8. Ex Q.1 (viii)
    A student uses spectacles of number -2 for seeing distant objects. Commonly used lenses for her/his spectacles are
    1. A.
      bi-concave
    2. B.
      double concave
    3. C.
      concavo-convex
    4. D.
      convexo-concave
  9. Ex Q.1 (ix)
    A spherical marble of refractive index 1.5 and curvature 1.5 cm, contains a tiny air bubble at its centre. Where will it appear when seen from outside?
    1. A.
      1 cm inside
    2. B.
      at the centre
    3. C.
      5/3 cm inside
    4. D.
      2 cm inside
  10. Ex Q.1 (x)
    Select the WRONG statement.
    1. A.
      Smaller angle of prism is recommended for greater angular dispersion.
    2. B.
      Right angled isosceles glass prism is commonly used for total internal reflection.
    3. C.
      Angle of deviation is practically constant for thin prisms.
    4. D.
      For emergent ray to be possible from the second refracting surface, certain minimum angle of incidence is necessary from the first surface.
  11. Ex Q.1 (xi)
    Angles of deviation for extreme colours are given for different prisms. Select the one having maximum dispersive power of its material.
    1. A.
      7∘, 10∘7^\circ,\ 10^\circ
    2. B.
      8∘, 11∘8^\circ,\ 11^\circ
    3. C.
      12∘, 16∘12^\circ,\ 16^\circ
    4. D.
      10∘, 14∘10^\circ,\ 14^\circ
  12. Ex Q.1 (xii)
    Which of the following is not involved in formation of a rainbow?
    1. A.
      refraction
    2. B.
      angular dispersion
    3. C.
      angular deviation
    4. D.
      total internal reflection
  13. Ex Q.1 (xiii)
    Consider following statements regarding a simple microscope: (P) It allows us to keep the object within the least distance of distant vision. (Q) Image appears to be biggest if the object is at the focus. (R) It is simply a convex lens.
    1. A.
      Only (P) is correct
    2. B.
      Only (P) and (Q) are correct
    3. C.
      Only (Q) and (R) are correct
    4. D.
      Only (P) and (R) are correct

Answer the following questions

Practice · 13
  1. 2. Answer the following questions.
    Ex Q.2 (i)
    As per recent development, what is the nature of light? Wave optics and particle nature of light are used to explain which phenomena of light, respectively?
  2. Ex Q.2 (ii)
    Which phenomena can be satisfactorily explained using ray optics? State the assumptions on which ray optics is based.
  3. Ex Q.2 (iii)
    What is focal power of a spherical mirror or of a lens? What may be the reason for using P=1fP = \dfrac{1}{f} as its expression?
  4. Ex Q.2 (iv)
    At which positions of the objects do spherical mirrors produce (i) diminished image, (ii) magnified image?
  5. Ex Q.2 (v)
    State the restrictions for having images produced by spherical mirrors to be appreciably clear.
  6. Ex Q.2 (vi)
    Explain spherical aberration for spherical mirrors. How can it be minimized? Can it be eliminated by some curved mirrors?
  7. Ex Q.2 (vii)
    Define absolute refractive index and relative refractive index. Explain in brief, with an illustration for each.
  8. Ex Q.2 (viii)
    Explain 'mirage' as an illustration of refraction.
  9. Ex Q.2 (ix)
    Under what conditions is total internal reflection possible? Explain it with a suitable example. Define critical angle of incidence and obtain an expression for it.
  10. Ex Q.2 (x)
    Describe construction and working of an optical fibre. What are the advantages of optical fibre communication over electronic communication?
  11. Ex Q.2 (xi)
    Why is a prism binoculars preferred over traditional binoculars? Describe its working in brief.
  12. Ex Q.2 (xii)
    A spherical surface separates two transparent media. Derive an expression that relates object and image distances with the radius of curvature for a point object. Clearly state the assumptions, if any.
  13. Ex Q.2 (xiii)
    Derive lens makers' equation. Why is it called so? Under which conditions focal length ff and radii of curvature RR are numerically equal for a lens?

Answer the following questions in detail

Practice · 12
  1. 2. Answer the following questions in detail.
    Ex Q.2b (i)
    What are different types of dispersions of light? Why do they occur?
  2. Ex Q.2b (ii)
    Define angular dispersion for a prism. Obtain its expression for a thin prism. Relate it with the refractive indices of the material of the prism for corresponding colours.
  3. Ex Q.2b (iii)
    Explain and define dispersive power of a transparent material. Obtain its expressions in terms of angles of deviation and refractive indices.
  4. Ex Q.2b (iv)
    (i) State the conditions under which a rainbow can be seen. (ii) Explain the formation of a primary rainbow. For which angular range with the horizontal is it visible? (iii) Explain the formation of a secondary rainbow. For which angular range with the horizontal is it visible? (iv) Is it possible to see primary and secondary rainbow simultaneously? Under what conditions?
  5. Ex Q.2b (v)
    (i) Explain chromatic aberration for spherical lenses. State a method to minimize or eliminate it. (ii) What is achromatism? Derive a condition to achieve achromatism for a lens combination. State the conditions for it to be converging.
  6. Ex Q.2b (vi)
    Describe spherical aberration for spherical lenses. What are different ways to minimize or eliminate it?
  7. Ex Q.2b (vii)
    Define and describe magnifying power of an optical instrument. How does it differ from linear or lateral magnification?
  8. Ex Q.2b (viii)
    Derive an expression for magnifying power of a simple microscope. Obtain its minimum and maximum values in terms of its focal length.
  9. Ex Q.2b (ix)
    Derive the expressions for the magnifying power and the length of a compound microscope using two convex lenses.
  10. Ex Q.2b (x)
    What is a terrestrial telescope and an astronomical telescope?
  11. Ex Q.2b (xi)
    Obtain the expressions for magnifying power and the length of an astronomical telescope under normal adjustments.
  12. Ex Q.2b (xii)
    What are the limitations in increasing the magnifying powers of (i) simple microscope (ii) compound microscope (iii) astronomical telescope?

Solve the following numerical examples

Practice · 13
  1. 3. Solve the following numerical examples.
    Ex Q.3 (i)
    A monochromatic ray of light strike the water (n=4/3)(n = 4/3) surface in a cylindrical vessel at angle of incidence 53053^{0}. Depth of water is 36 cm. After striking the water surface, how long will the light take to reach the bottom of the vessel? [Angles of the most popular Pythagorean triangle of sides in the ratio 3:4:5 are nearly 37037^{0}, 53053^{0} and 90090^{0}]
  2. Ex Q.3 (ii)
    Estimate the number of images produced if a tiny object is kept in between two plane mirrors inclined at 35035^{0}, 36036^{0}, 40040^{0} and 45045^{0}.
  3. Ex Q.3 (iii)
    A rectangular sheet of length 30 cm and breadth 3 cm is kept on the principal axis of a concave mirror of focal length 30 cm. Draw the image formed by the mirror on the same ray diagram, as far as possible on scale.
  4. Ex Q.3 (iv)
    A car uses a convex mirror of curvature 1.2 m as its rear-view mirror. A minibus of cross section 2.4 m×2.4 m2.4\ \text{m} \times 2.4\ \text{m} is 6.6 m away from the mirror. Estimate the image size.
  5. Ex Q.3 (v)
    A glass slab of thickness 2.5 cm having refractive index 5/3 is kept on an ink spot. A transparent beaker of very thin bottom, containing water of refractive index 4/3 up to 8 cm, is kept on the glass block. Calculate apparent depth of the ink spot when seen from the outside air.
  6. Ex Q.3 (vi)
    A convex lens held some distance above a 6 cm long pencil produces its image of SOME size. On shifting the lens by a distance equal to its focal length, it again produces the image of the SAME size as earlier. Determine the image size.
  7. Ex Q.3 (vii)
    Figure below shows the section ABCD of a transparent slab. There is a tiny green LED light source at the bottom left corner B. A certain ray of light from B suffers total internal reflection at nearest point P on the surface AD and strikes the surface CD at point Q. Determine refractive index of the material of the slab and distance DQ. At Q, the ray PQ will suffer partial or total internal reflection? [You may use the approximation given in Q 1 above]. [Figure: ABCD is a rectangle drawn with A at the top left, D at the top right, B at the bottom left and C at the bottom right. The bottom edge BC measures 6 cm and the right-hand edge from D down to C measures 3 cm. P is marked on the top edge AD with AP = 4 cm, and Q is marked on the right-hand edge DC. The approximation referred to is the one stated in numerical (i) above: the angles of the 3:4:5 Pythagorean triangle are nearly 37037^{0}, 53053^{0} and 90090^{0}.]
  8. Ex Q.3 (viii)
    A point object is kept 10 cm away from one of the surfaces of a thick double convex lens of refractive index 1.5 and radii of curvature 10 cm and 8 cm. Central thickness of the lens is 2 cm. Determine location of the final image considering paraxial rays only. Hint : Single spherical surface formula to be used twice.
  9. Ex Q.3 (ix)
    A monochromatic ray of light is incident at 37037^{0} on an equilateral prism of refractive index 3/2. Determine angle of emergence and angle of deviation. If angle of prism is adjustable, what should its value be for emergent ray to be just possible for the same angle of incidence.
  10. Ex Q.3 (x)
    From the given data set, determine angular dispersion by the prism and dispersive power of its material for extreme colours. nR=1.62n_{R} = 1.62, nV=1.66n_{V} = 1.66, δR=3.1∘\delta_{R} = 3.1^\circ
  11. Ex Q.3 (xi)
    Refractive index of a flint glass varies from 1.60 to 1.66 for visible range. Radii of curvature of a thin convex lens are 10 cm and 15 cm. Calculate the chromatic aberration between extreme colours.
  12. Ex Q.3 (xii)
    A person uses spectacles of 'number' 2.00 for reading. Determine the range of magnifying power (angular magnification) possible. It is a concavo-convex lens (n=1.5)(n = 1.5) having curvature of one of its surfaces to be 10 cm. Estimate that of the other.
  13. Ex Q.3 (xiii)
    Focal power of the eye lens of a compound microscope is 6 dioptre. The microscope is to be used for maximum magnifying power (angular magnification) of at least 12.5. The packing instructions demand that length of the microscope should be 25 cm. Determine minimum focal power of the objective. How much will its radius of curvature be if it is a biconvex lens of n=1.5n = 1.5.