In a diffraction pattern due to a narrow slit of width a, alternate dark and bright fringe pattern is obtained on a screen kept at distance D from the slit. Choose the correct option.

(A) The angular width of central maximum is given by 2D/a, linear width is given by 2Dλ/a
(B) When the size of aperture, a is quite large, the diffraction effect is negligible,
(C) For light of smaller wavelength, angular width of central maximum increases, while linear width decreases,
(D) Angular width of central maximum does not decrease while linear width decreases on decreasing distance of screen from slit.

Choose the correct answer from the options given below:

(B) and (D) only

The correct answer is Option (4) → (B) and (D) only

Diffraction by a single slit: The central maximum is the widest and brightest part of the diffraction pattern.

Formula for angular width (θ) of central maximum is:

$\theta = \frac{2\lambda}{a}$

Linear width on screen placed at distance D is:

$w = 2D \cdot \frac{\lambda}{a}$

Now, analyzing options:

(A) Angular width is $2\lambda/a$ not $2D/a$ → Incorrect

(B) Larger aperture (a ↑) means θ ↓ ⇒ Less noticeable diffraction → Correct

(C) If λ ↓ ⇒ θ ↓ and linear width $w ↓$ → So, angular width also decreases → Incorrect

(D) Linear width $w = 2Dλ/a$ decreases as D ↓, but angular width remains constant (since independent of D) → Correct