In a Fraunhoffer diffraction at single slit of width 'a' with incident light of wavlength of 5500 Å, the first minimum is observed, at an angle of `30^(@)`. At what angle the first secondary maximum is observed?

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

For the first minimum, `a sintheta=lamda" "therefore a sin30^(@)=lamda`
`therefore a/2=lamda or a=2lamda`
and for the secondary maximum
`asin theta'=(2n+1)/(lamda)/(2)`
`therefore sintheta'=(2n+1)lamda)/(2a)=(3lamda)/(2a)` for n=1)
`sintheta'=(3lamda)/(2xx2lamda)=(3)/(4)`
`therefore theta'=sin^(-1)((3)/(4))`.