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

Answer

C

Explanation

Condition for nth secondary maximum, path difference
`=a sin theta_(n)=n lambda`
Condition for nth secondary maximum, part difference
`=a sin theta_(n)=(2n+1)(lambda)/(2)`
For 1st minimu, `lambda=5500" Å " and theta_(n)=30^(@)`
Path difference, `a sin30^(@)=lambda " "`...(i)
For 2nd maximum,
Path difference `a sin theta_(n)=(2+1)(lambda)/(2)=(3lambda)/(2) " "` (ii)
Dividing Eq. (i) by Eq. (ii), we get
`((1)/(2))/(sin theta_(n))=(2)/(3) rArr sin theta_(n)=(3)/(4) rArr theta_(n)=sin^(-1)((3)/(4))`