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

Options

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

Answer

A

Explanation

`a=sin 30^(@)=1implies a=2lambda`
`1st` secondary maximum
`a sin theta_(1)=(3lambda)/2 sin theta_(1)=(3lambda//2)/(2 lambda)=3/4`
`theta_(1)=sin^(-1)(3//4)`