A prism of refractive index p and angle A is placed in the minimum deviation position. If the angffe of minimum deviation is A, then the value of A in terms of p is

Options

A. `sin ^(-2)((mu)/(2))`
B. `sin^(-1)sqrt((mu-1)/(2))`
C. `2 cos^(-1)((mu)/(2))`
D. `cos^(-1)((mu)/(2))`

Answer

C

Explanation

Given `delta_(m)=A,` as `mu=(sin((A+delta_(m))/(2)))/(sin((A)/(2)))`
`impliesmu=(sin((A+delta_(m))/(2)))/(sin((A)/(2)))=2cos((A)/(2))impliesA=cos^(-1)((mu)/(2))`