The refracting angle of a prism is `A` and refractive index of the material of the prism is `cos(A//2)`. The angle of minimum deviation is

Options

A. `180^(@)-3A`
B. `180^(@)-2A`
C. `90^(@)-A`
D. `180^(@)+2A`

Answer

B

Explanation

The refractive index of the material of the prism
`mu=(sin .(A+delta_(m))/(2))/(sin .(A)/(2))`
`impliescot.(A)/(2)=((sin(A+delta_(m)))/(2))/(sin .(A)/(2))`
`sin((A+delta_(m))/(2))=cot.(A)/(2)sin .(A)/(2)`
`sin ((A+delta_(m))/(2))=(cos.(A)/(2))/(sin .(A)/(2))sin .(A)/(2)`
`sin ((A+delta_(m))/(2))=sin ((pi)/(2)-(A)/(2))`
`implies(A+delta_(m))/(2)=(pi)/(2)-(A)/(2)`
`A+delta_(m)=pi -Aimpliesdelta_(m)=180-2A`