A prism of apex angle `A=60^@` has the refractive index `mu=sqrt2.` The angle of incidence for minimum deviation is

Options

A. `45^@`
B. `60^@`
C. `30^@`
D. `si n^-1(2)/(3)`

Answer

A

Explanation

`mu=(sini)/(sinr)=(sini)/(sin(A//2))=(sini)/(sin(60^@//2))=(sini)/(1//2)`
`sqrt2=(sini)/((1//2))impliessini=1/sqrt2=sin45^@impliesi=45^@`
OR

When `delta=delta_m`, refracted ray inside prism is parallel to base
Refracted at AB:
`1xxsini=musin30^@=sqrt2xx1/2=1/sqrt2=sin45^@`
`i=45^@`