Wave Optics: 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. State Huygens principle.
2. Define coherent sources.
3. Write the condition for a dark fringe in YDSE.
4. Why is the central fringe white with white light?
5. What happens to β in a liquid?
6. Write the angular width of the central maximum.
7. What is a polaroid?
8. Intensity through crossed polaroids?
9. Phase difference for path difference λ/2?
10. Give one use of polaroids.

D. Short answer I (2 marks each)

1. Draw the wavefront shapes for a point source, a line source and a distant source.
2. Derive I = 4I₀cos²(φ/2).
3. d = 0.5 mm, D = 1 m, λ = 600 nm: find β and the position of the 3rd bright fringe.
4. Give two differences between interference and diffraction.
5. Why are coherent sources necessary for interference?
6. A slit of 0.1 mm, λ = 500 nm, D = 2 m: width of the central maximum.
7. Unpolarised light of 20 W/m² through polaroids at 45°: final intensity.
8. Explain why sound bends round corners more than light.

Rough work

E. Short answer II (3 marks each)

1. Use Huygens' principle to verify Snell's law of refraction.
2. Derive the expression for fringe width in YDSE.
3. Explain the formation of the central maximum, minima and secondary maxima in single-slit diffraction.
4. Two wavelengths 450 nm and 600 nm in YDSE (d = 0.5 mm, D = 1.5 m): least distance where bright fringes coincide.
5. A polaroid is rotated between two crossed polaroids. Show that the intensity is (I₀/4)sin²2θ.
6. Two waves of intensities I and 4I interfere. Find I_max and I_min.

F. Long answer (5 marks each)

1. Describe YDSE. Derive the positions of bright and dark fringes and β. How does the pattern change if (a) the set-up is in water, (b) one slit is covered by a thin glass sheet?
2. State Huygens principle. Use it to verify the laws of reflection and refraction. Explain the behaviour of a plane wave through a convex lens.
3. Discuss single-slit diffraction with the intensity graph. Compare with interference. A slit of width a gives the first minimum at 30° for 600 nm: find a and the angle of the first secondary maximum.

G. HOTS (higher-order thinking)

1. In YDSE, what happens if the two slits are replaced by two separate bulbs? Why?
2. Where does the energy go at the dark fringes?
3. Why can't we see diffraction from a large door with light?
4. Explain why polaroid sunglasses reduce glare from roads and water.

20 MCQs

1. Wavefront from a point source
   (a) plane (b) cylindrical (c) spherical (d) parabolic
2. Rays and wavefronts are
   (a) perpendicular (b) parallel (c) at 45° (d) unrelated
3. Fringe width
   (a) λd/D (b) λ/dD (c) Dd/λ (d) λD/d
4. Two waves of intensity I₀ in phase give
   (a) 2I₀ (b) 4I₀ (c) I₀ (d) zero
5. Path difference λ/3 with equal intensities I₀
   (a) 2I₀ (b) I₀ (c) 3I₀ (d) 0
6. Average intensity in an interference pattern
   (a) 4I₀ (b) 0 (c) I₀ (d) 2I₀
7. Coherent sources have
   (a) constant phase difference (b) same amplitude (c) different frequency (d) random phase
8. Single slit first minimum
   (a) a sin θ = λ/2 (b) d sin θ = λ (c) a sin θ = λ (d) a = λ
9. Central maximum width (linear)
   (a) λD/a (b) 2a/λD (c) λa/D (d) 2λD/a
10. YDSE in water: β
    (a) increases (b) decreases (c) unchanged (d) zero
11. Malus' law
    (a) I₀cos θ (b) I₀sin²θ (c) I₀cos²θ (d) I₀/2
12. Unpolarised light through one polaroid
    (a) halves (b) unchanged (c) zero (d) quarters
13. Polarisation proves light is
    (a) longitudinal (b) transverse (c) particles (d) EM only
14. Bright fringe phase difference
    (a) (2n+1)π (b) nπ/2 (c) 2nπ (d) π/2
15. If d is doubled, β becomes
    (a) 2β (b) β (c) 4β (d) β/2
16. Huygens' secondary wavelets travel at
    (a) the speed of the wave (b) c always (c) half the speed (d) zero
17. Diffraction is more noticeable when the obstacle size is
    (a) comparable to λ (b) much larger than λ (c) zero (d) infinite
18. Crossed polaroids transmit
    (a) I₀ (b) I₀/2 (c) I₀/4 (d) nothing
19. Shape of YDSE fringes for D ≫ d
    (a) circular (b) nearly straight (c) parabolic (d) elliptical
20. λ of 600 nm light in glass (n = 1.5)
    (a) 600 nm (b) 900 nm (c) 400 nm (d) 300 nm

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: Two independent bulbs do not give interference. R: They are not coherent.
2. A: The fringe width in YDSE decreases in water. R: The wavelength of light decreases in water.
3. A: The central maximum of a single slit is the brightest. R: All parts of the slit send light in phase to the centre.
4. A: Sound can be polarised. R: Sound is a longitudinal wave.
5. A: Light added to light can produce darkness. R: Destructive interference of coherent waves gives darkness.
6. A: A polaroid halves the intensity of unpolarised light. R: It transmits only the component of E along its pass axis.

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

Answers to the practice set