In a diffraction pattern due to single slit of width `'a'`, the first minimum is observed at an angle `30^(@)` when light of wavelength `5000 Å` is inclined on the slit. The first secondary maximum is observed at an angle of:

Options

A. `sin^(-1)(2//3)`
B. `sin^(-1)(1//2)`
C. `sin^(-1)(3//4)`
D. `sin^(-1)(1//4)`

Answer

C

Explanation

For first minimum,
`a sin theta = 1 lambda` or `a sin 30^(@) = lambda` or `(a)/(2) = lambda`
For first secondary maximum
`a sin theta' = (2n + 1)(lambda)/(2) = (3 lambda)/(2)`
`sin theta' = (3 lambda)/(2 a) = (3 lambda)/(2 xx 2 lambda) = (3)/(4)`
`theta' = sin^(-1)(3//4)`