Ray Optics and Optical Instruments: Class 12 Important Questions with Answers

Practice set: test yourself

Try every question before looking at the answers below. 64 or more out of 80 means you are ready for the board.

C. Very short answer (1 mark each)

1. Write two conditions for TIR.
2. Why does a straw look bent in water?
3. State the Cartesian sign convention for u.
4. Write the lens maker's formula.
5. Define 1 dioptre.
6. Why are convex mirrors used as rear-view mirrors?
7. Write the relation between n, A and δ_m.
8. Magnifying power of a simple microscope at D?
9. What is the tube length of a telescope in normal adjustment?
10. Name one use of optical fibres.

D. Short answer I (2 marks each)

1. An object 20 cm from a concave mirror (f = 15 cm). Image?
2. Find the critical angle for diamond (n = 2.42).
3. A convex lens of f = 20 cm and a concave lens of f = 10 cm in contact. Power and nature?
4. Find the apparent depth of a coin under 20 cm of water.
5. Draw the δ–i graph for a prism and mark δ_m.
6. Explain the working of an optical fibre.
7. A 2 cm object is 15 cm from a convex lens of f = 10 cm. Image size?
8. A telescope has f_o = 100 cm and f_e = 5 cm. Find m in normal adjustment and at 25 cm.

Rough work

E. Short answer II (3 marks each)

1. Derive the mirror formula for a concave mirror.
2. Derive the relation for refraction at a convex spherical surface.
3. Derive the formula for two thin lenses in contact.
4. Show that n = sin((A + δ_m)/2)/sin(A/2).
5. A small fish 1 m deep in a pond (n = 4/3). Radius of the circle through which it sees the outside world?
6. A compound microscope: f_o = 1 cm, f_e = 5 cm, object at 1.1 cm, final image at 25 cm. Find m and the lens separation.

F. Long answer (5 marks each)

1. Derive the lens maker's formula. A glass lens (n = 1.5) has f = 20 cm in air: find f in water (n = 4/3).
2. Draw the ray diagram of a compound microscope with the final image at D and derive its magnifying power. Why must both lenses have small f?
3. Explain refraction through a prism with a diagram; derive δ = i + e − A and the prism formula. A prism of A = 60° has δ_m = 38°: find n.
4. Draw a refracting telescope in normal adjustment and derive m. Compare it with a reflecting telescope. A telescope has m = 40 and tube 82 cm: find f_o and f_e.

G. HOTS (higher-order thinking)

1. A lens is cut in half along its principal axis. How do the focal length and the brightness of the image change?
2. Why does the Sun look oval at sunrise? (Link to refraction in the atmosphere.)
3. A virtual image cannot be caught on a screen; can it be photographed? Why?
4. Why is the objective of a telescope given a large aperture?

20 MCQs

1. Focal length of a mirror of R = 30 cm
   (a) 30 cm (b) 60 cm (c) 15 cm (d) 7.5 cm
2. m = −2 for a mirror means
   (a) concave, real (b) convex, virtual (c) concave, virtual (d) convex, real
3. Critical angle for glass (n = 1.5) about
   (a) 30° (b) 60° (c) 48° (d) 42°
4. Power of a lens of f = −50 cm
   (a) +2 D (b) −2 D (c) −0.5 D (d) +0.5 D
5. Convex lens in a liquid of the same n
   (a) converges more (b) behaves as a plane sheet (c) diverges (d) magnifies
6. Lens formula
   (a) 1/v + 1/u = 1/f (b) uv = f (c) v − u = f (d) 1/v − 1/u = 1/f
7. At δ_m, the ray inside a prism is
   (a) parallel to the base (b) along a face (c) normal to the base (d) along the axis
8. δ for a thin prism
   (a) nA (b) (n + 1)A (c) (n − 1)A (d) A/n
9. TIR is not involved in
   (a) optical fibre (b) mirage (c) diamond (d) twinkling of stars
10. Telescope f_o = 120 cm, f_e = 4 cm: m in normal adjustment
    (a) 124 (b) 30 (c) 480 (d) 116
11. For large magnification a microscope needs
    (a) large f_o, f_e (b) large f_o (c) small f_o, f_e (d) large f_e only
12. Apparent depth of 12 cm water (n = 4/3)
    (a) 9 cm (b) 16 cm (c) 12 cm (d) 6 cm
13. Convex mirror image is always
    (a) real, inverted (b) virtual, erect, diminished (c) virtual, enlarged (d) real, erect
14. Wavelength of 600 nm light in glass of n = 1.5
    (a) 900 nm (b) 600 nm (c) 400 nm (d) 300 nm
15. Lenses of +4 D and −2 D in contact: f
    (a) 16.7 cm (b) 25 cm (c) −50 cm (d) 50 cm
16. Magnifying power of a simple microscope (image at ∞)
    (a) D/f (b) 1 + D/f (c) f/D (d) Df
17. Object at the centre of curvature of a concave mirror: image
    (a) at C, inverted, same size (b) at F (c) at ∞ (d) virtual
18. Cassegrain secondary mirror is
    (a) plane (b) concave (c) parabolic concave (d) convex
19. Equiconvex lens, n = 1.5, R = 20 cm: f
    (a) 10 cm (b) 20 cm (c) 40 cm (d) 30 cm
20. For TIR light must go
    (a) rarer → denser (b) denser → rarer at i < i_c (c) denser → rarer at i > i_c (d) at any angle

1 (c) · 2 (a) · 3 (d) · 4 (b) · 5 (b) · 6 (d) · 7 (a) · 8 (c) · 9 (d) · 10 (b) · 11 (c) · 12 (a) · 13 (b) · 14 (c) · 15 (d) · 16 (a) · 17 (a) · 18 (d) · 19 (b) · 20 (c)

Assertion–Reason (6)

(a) Both true, R explains A. (b) Both true, R does not explain A. (c) A true, R false. (d) A false, R true.

1. A: A convex lens immersed in a liquid of the same n disappears. R: No refraction occurs at its surfaces.
2. A: Diamond sparkles. R: Its critical angle is small, about 24°.
3. A: The magnifying power of a compound microscope is negative. R: The final image is erect.
4. A: Reflecting telescopes have no chromatic aberration. R: Chromatic aberration arises only from refraction.
5. A: The focal length of a lens is the same for all colours. R: n depends on wavelength.
6. A: Rear-view mirrors are convex. R: A convex mirror gives a wide field of view.

Key: 1 (a) · 2 (a) · 3 (c) · 4 (a) · 5 (d) · 6 (a)

Answers to the practice set