In a Fraunhofer diffraction experiment at single slit using a light of wavelength 400 nm , the first minimum is formed at an angle of `30^(@)` . The direction `theta` of the first secondary maximum is given by

Options

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

Answer

D

Explanation

For Fraunhofer diffraction at single slit , the equation for secondary maxima is given by `sintheta=((2n+1)lambda)/(2a)`.
For the `(1^(st))` secondary minima , `asintheta=1lambda`.
I.e ,`lambda//asintheta=sin30^(@)=1//2`
`thereforesintheta` for secondary maxima `=(2n+1)/(2).(1)/(2)=(2n+1)/(4)`.
`thereforethetasin^(-1)((2n+1)/(4))=sin^(-1)((3)/(4))`