Question

In a fraunhofer diffraction by single slit of width d with incident light of wavelength 5500 Å the first minimum is observed at angle of 30°. The first secondary maximum is observed at an angle θ = ___________ .

(A) sin^–1(1 / √2)

(B) sin^–1(3 / 4)

(C) sin^–1(√3 / 2)

(D) sin^–1(1 / 4)

Answer 1

The correct option is  (B) sin^–1(3/4)

Explanation:

First minimum occurs at θ then sin θ = (λ/a)

∴ sin 30 = (λ/a) i.e. (λ/a) = (1/2)   (1)

First secondary maxima occurs at θ' then sin θ' = {n + (1/2)} (λ/a) where n = 1 

∴ sin θ' = {1 + (1/2)} (λ/a) = (3/2) × (1/2) = (3/4) 

θ' = sin^–1(3 / 4)