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 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= lambda " " [ n=1]`
`:. a sin 30^(@) = lambda`
`:. a xx(1)/(2)= lambda`
For first maximum,
`a sin theta_(1)=(2n+)(lambda)/(2)`
`:. a sin theta_(1)=(3lambda)/(2)`
`:. sin theta_(1)=(3lambda)/(2)`
`:. sin theta_(1)=(3)/(4)`
`:. theta_(1)=sin^(-1)((3)/(4))`