Question

Read the following:
(A) The width of the central band in a diffraction pattern.
(B) The width of the first bright band in the diffraction pattern.
(C) The width of the central band in the diffraction pattern if D is doubled.
(D) The width of the first bright band in the diffraction pattern if D is tripled.
Choose the correct answer from the options given below in increasing order of width.

• A. (A), (B), (D), (C)
• B. (A), (C), (D), (B)
• C. (C), (A), (D), (B)
• D. (B), (A), (D), (C)

Answer 1

The Correct Option is D

In single-slit diffraction, the width of any band (central or bright) is given by:

\[ w = \frac{λD}{d} \]

where: 
λ = wavelength of light 
D = distance between slit and screen 
d = slit width

Analysis of each case:

A. Central band width (original): \( w_A = \frac{2λD}{d} \) (central band is twice as wide as others)

B. First bright band width (original): \( w_B = \frac{λD}{d} \)

C. Central band width with doubled D: \( w_C = \frac{2λ(2D)}{d} = \frac{4λD}{d} \)

D. First bright band width with tripled D: \( w_D = \frac{λ(3D)}{d} = \frac{3λD}{d} \)

Width Comparison:

1. Original first bright band (B): \( \frac{λD}{d} \)

2. Original central band (A): \( \frac{2λD}{d} \)

3. First bright band with tripled D (D): \( \frac{3λD}{d} \)

4. Central band with doubled D (C): \( \frac{4λD}{d} \)

Increasing Order: B < A < D < C