JEE Physics Wave Optics MCQs Set 22

Answer: (b) \( \sqrt{3}\times10^8\ \text{m s}^{-1} \)

Explanation:
1. μ = tan 60° = √3.
2. v = c/μ = 3 × 10⁸/√3 = √3 × 10⁸ m/s.

Teacher's Note:
1. Recall the basic fact.

Answer: (d) 0.2 mm

Explanation:
1. Central maximum width of single slit = 2λD/a.
2. This must equal 10 fringe widths = 10λD/d.
3. So a = d/5 = 0.2 mm.

Teacher's Note:
1. Recall the basic fact.

Answer: (b) \( \sin^{-1}\left(\frac{2}{5}\right) \)

Explanation:
1. a = 2.5 × 10⁻⁴ cm = 2.5 × 10⁻⁶ m.
2. a sinθ = 2λ gives sinθ = 2 × 5 × 10⁻⁷/2.5 × 10⁻⁶ = 0.4 = 2/5.
3. θ = sin⁻¹(2/5).

Teacher's Note:
1. Recall the basic fact.

Answer: (b) 486 nm

Explanation:
1. β is proportional to λ.
2. λ₂ = 540 × 8.1/9.0 = 486 nm.

Teacher's Note:
1. Recall the basic fact.

Answer: (b) white

Explanation:
1. At the centre the path difference is zero for every colour.
2. So all colours give a bright fringe and the central fringe is white.

Teacher's Note:
1. Recall the basic fact.

Answer: (b) 2 times

Explanation:
1. β is proportional to λ.
2. λred/λviolet = 7000/4000 ≈ 2.

Teacher's Note:
1. Recall the basic fact.

Answer: (d) I and III

Explanation:
1. The central maximum is twice as wide as the others and intensity falls outwards.
2. The first null is at λ/a and the secondary bands have equal width, so II and IV are false.

Teacher's Note:
1. Recall the basic fact.

Answer: (b) focused to a spot of finite area because of diffraction

Explanation:
1. Even an ideal lens has a finite aperture.
2. Diffraction at the aperture spreads the image into a spot of finite size (Airy disc).

Teacher's Note:
1. Recall the basic fact.

Answer: (c) unpolarised

Explanation:
1. A quarter wave plate only introduces a fixed phase difference between two components.
2. Unpolarised light has no fixed relation between components, so it remains unpolarised.

Teacher's Note:
1. A wave plate cannot polarise unpolarised light.

Answer: (a) 0°

Explanation:
1. The plane of polarisation contains the direction of propagation, so the angle between them is 0°.

Teacher's Note:
1. Recall the basic fact.

Answer: (d) infinity

Explanation:
1. Diffraction at a slit is the interference of secondary wavelets from an infinite number of coherent points on the wavefront.

Teacher's Note:
1. Recall the basic fact.

Answer: (c) \( 90^\circ \)

Explanation:
1. At Brewster's angle the reflected and refracted rays are perpendicular, so the angle is 90°.

Teacher's Note:
1. Recall the basic fact.

Answer: (b) \( \frac{I}{2} \)

Explanation:
1. I = Imax cos²(φ/2) with Imax = I.
2. For λ/4, φ = π/2, so I' = I cos²(π/4) = I/2.

Teacher's Note:
1. Recall the basic fact.

Answer: (b) 0.16°

Explanation:
1. θ = λ/2d = 5.46 × 10⁻⁷/(2 × 10⁻⁴) = 2.73 × 10⁻³ rad.
2. In degrees: 2.73 × 10⁻³ × 57.3° ≈ 0.16°.

Teacher's Note:
1. Recall the basic fact.

Answer: (a) 6000 Å

Explanation:
1. Path shift = (μ − 1)t = 0.5 × 6 × 10⁻⁶ = 3 × 10⁻⁶ m = 5λ.
2. λ = 6 × 10⁻⁷ m = 6000 Å.

Teacher's Note:
1. Recall the basic fact.

Answer: (c) \( I_0/4 \)

Explanation:
1. After A the intensity is I₀/2.
2. After B: (I₀/2)cos²45° = I₀/4.

Teacher's Note:
1. Recall the basic fact.

Answer: (a) I, II and III

Explanation:
1. Sustained interference needs a constant phase difference, nearly equal amplitudes and equal frequency.
2. Opposite directions of motion are not required.

Teacher's Note:
1. Recall the basic fact.

Answer: (a) General illumination

Explanation:
1. Separate lamps are incoherent, so their phase difference changes randomly.
2. The screen shows general illumination without fringes.

Teacher's Note:
1. Recall the basic fact.

Answer: (a) violet

Explanation:
1. Fringe width is proportional to wavelength.
2. Violet has the smallest wavelength, so its first bright fringe is nearest to the centre.

Teacher's Note:
1. Recall the basic fact.

Answer: (d) invisible

Explanation:
1. The two beams have different wavelengths and are not coherent.
2. No interference pattern is seen.

Teacher's Note:
1. Recall the basic fact.

Answer: (b) plane polarised

Explanation:
1. A nicol prism produces plane polarised light.

Teacher's Note:
1. Recall the basic fact.

Answer: (c) K/2

Explanation:
1. Path difference λ gives a maximum, so Imax = K.
2. Path difference λ/4 gives φ = π/2, so I = K cos²(π/4) = K/2.

Teacher's Note:
1. Recall the basic fact.

Answer: (b) bends upwards

Explanation:
1. Light travels faster in the lower part where the refractive index is smaller.
2. The lower part of the wavefront moves ahead, so the beam bends upwards.

Teacher's Note:
1. Recall the basic fact.

Answer: (b) decrease in width

Explanation:
1. Wavelength in water is λ/μ, which is smaller.
2. Since β = λD/d, the fringe width decreases.

Teacher's Note:
1. Recall the basic fact.

Answer: (d) 7248 Å

Explanation:
1. The first secondary maximum is at a sinθ = 3λ/2.
2. λ = 2 × 0.012 × 10⁻³ × 0.0906/3 = 7.248 × 10⁻⁷ m = 7248 Å.

Teacher's Note:
1. Recall the basic fact.