A parallel beam of monochromatic light of wavelength 900 nm passes through a long slit of width 0.4 mm. The angular divergence in which most of the light is diffracted, is

$4.5 × 10^{-3} rad$

The correct answer is Option (4) → $4.5 × 10^{-3} rad$

Given:

Wavelength, $λ = 900\ \text{nm} = 9 \times 10^{-7}\ \text{m}$

Slit width, $a = 0.4\ \text{mm} = 4 \times 10^{-4}\ \text{m}$

For single-slit diffraction, the first minimum occurs at:

$a\sinθ = λ$

∴ $\sinθ = \frac{λ}{a} = \frac{9 \times 10^{-7}}{4 \times 10^{-4}} = 2.25 \times 10^{-3}$

Since $θ$ is small, $\sinθ ≈ θ$ (in radians):

$θ = 2.25 \times 10^{-3}\ \text{rad}$

Angular divergence for central maximum = $2θ = 2 \times 2.25 \times 10^{-3} = 4.5 \times 10^{-3}\ \text{rad}$

Answer: Angular divergence = $4.5 \times 10^{-3}\ \text{rad}$