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

As the first minimum is observed at an angle of `30^(@)` in a diffraction pattern due to a single slit of width a
i.e., `n=1 theta=30^(@)`
`because` According to Bragg's law of diffraction
`a sin theta =nlambda rArr a sin 30^(@)=(1)lambda`
`rArra=2lambda...(1)[because sin 30^(@)=1/2]`
For 1st secondary maxima
`rArr a sin theta_(1)=(3lambda)/2rArrsin theta_(1)=(3lambda)/(2a)...(ii)`
Substitute value of a from Eq. (i) to Eq. (ii) we get
`sin theta_(1)=(3lambda)/(4lambda)rArrsin theta_(1)=3/4rArrtheta_(1)="sin"^(-1)(3/4)`