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

Answer

C

Explanation

From snell's law, Refractive index of material of prism is given by,
`mu=sin((A+Dm)/2)/sin(A/2)`
But `D_(m)=A`
`mu=sin((A+A)/2)/sin(A/2)=sin(A)/sin(A/2)=(2sin(A/2)cos(A/2))/sin(A/2)`
`implies cos(A/2)- mu/2`
`implies A/2=cos^(-1)(mu/2)`
`therefore A=2cos^(-1)(mu/2)`