JEE Physics Wave Optics MCQs Set 20

Answer: (a) 5000 Å

Explanation:
1. y = 3λf/a, so λ = ya/(3f) = 5 × 10⁻³ × 3 × 10⁻⁴/3 = 5 × 10⁻⁷ m = 5000 Å.

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

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. The path difference d sinθ ≤ d, so nλ ≤ d and the number of fringes is limited.
2. The reason therefore explains the assertion.

Teacher's Note:
1. The path difference is at most d.

Answer: (d) 1/3

Explanation:
1. After rotation, A: IA cos²30° = 3IA/4 and B: IB sin²30° = IB/4.
2. Equal brightness gives 3IA/4 = IB/4, so IA/IB = 1/3.

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

Answer: (a) 8

Explanation:
1. Number of fringes is proportional to 1/λ.
2. N = 10 × 4000/5000 = 8.

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

Answer: (b) is a geometrical method to find a wavefront

Explanation:
1. Huygens' principle is a geometrical method of finding the new wavefront from the old one.

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

Answer: (b) I and II

Explanation:
1. I and II are true.
2. A small portion of a sphere looks plane only at a large distance from the source, so III is false.

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

Answer: (b) separation of slits

Explanation:
1. β = λD/d.
2. Decreasing the slit separation d increases β.

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

Answer: (d) A is false, but R is true.

Explanation:
1. Interference can be studied with unequal intensities, so the assertion is false.
2. Unequal intensity makes the minima non-zero and reduces the clarity, so the reason is true.

Teacher's Note:
1. Unequal intensity reduces contrast but does not stop interference.

Answer: (c) II and III

Explanation:
1. Light has a much shorter wavelength than sound and is far smaller than ordinary obstacles.
2. So light does not bend round the wall, while sound does.

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

Answer: (c) wave front

Explanation:
1. The locus of points vibrating in the same phase is a wavefront.

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

Answer: (c) 3

Explanation:
1. Bright spots occur where d sinθ = nλ, so sinθ = n × 10⁻³.
2. Maximum θ = 0.06° = 1.05 × 10⁻³ rad, so n can be −1, 0, 1.
3. Hence 3 bright spots.

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

Answer: (a) 0.36 degree

Explanation:
1. Angular width = 2λ/a = 2 × 6.328 × 10⁻⁷/2 × 10⁻⁴ = 6.33 × 10⁻³ rad.
2. In degrees this is about 0.36°.

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

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. For θ = 180° (backward direction) the factor 1 + cosθ is zero.
2. So the amplitude of the backward wavelet vanishes, which explains the assertion.

Teacher's Note:
1. Link the inclination factor to the absence of a backward wave.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Yellow light has a shorter wavelength than red.
2. Since β is proportional to λ, the fringes become narrower.

Teacher's Note:
1. Fringe width depends directly on the wavelength.

Answer: (c) 1.625 mm

Explanation:
1. Third dark fringe: y = 2.5λD/d = 1.625 mm.
2. Fifth bright fringe: y = 5λD/d = 3.25 mm.
3. Difference = 1.625 mm.

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

Answer: (c) yellow and black

Explanation:
1. Sodium light is almost purely yellow.
2. The bright fringes are yellow and the dark fringes are black.

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

Answer: (b) Equal intensity

Explanation:
1. Equal intensity is not essential; it only improves the contrast.
2. Equal wavelength and a constant phase relationship are necessary.

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

Answer: (a) \( V=\frac{I_{max}-I_{min}}{I_{max}+I_{min}} \)

Explanation:
1. Visibility is defined as (Imax − Imin)/(Imax + Imin).

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

Answer: (d) 6000 Å

Explanation:
1. Δβ = λ ΔD/d, so λ = Δβ d/ΔD = (10⁻³ × 3 × 10⁻⁵)/(5 × 10⁻²) = 6 × 10⁻⁷ m = 6000 Å.

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

Answer: (c) I and II only

Explanation:
1. I and II are true.
2. The first minimum occurs at λ/2a, not λ/a, so III is false.

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

Answer: (c) 500 nm

Explanation:
1. Path difference = d y/D = (0.5 × 10⁻³ × 1.0 × 10⁻³)/0.5 = 1000 nm.
2. Strong intensity needs 1000 nm = nλ.
3. n = 2 gives λ = 500 nm (n = 1 gives 1000 nm and n = 3 gives 333 nm, both outside the visible range).

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

Answer: (b) 90°

Explanation:
1. The plane of polarisation is perpendicular to the plane of vibration.

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

Answer: (c) are transverse

Explanation:
1. Polarisation is possible only for transverse waves.

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

Answer: (b) downwards

Explanation:
1. The central fringe is where the optical paths from both slits are equal.
2. The path through B is longer, so the point must lie nearer to B to compensate, that is, the pattern shifts downwards.

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

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. The gaps in the muslin act as fine slits.
2. Different colours diffract through different angles and give a coloured spectrum.

Teacher's Note:
1. Muslin cloth acts like a grating.