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

D

Explanation

`mu=(sin((A+delta_m)/(2)))/(sin(A/2))`
`cot(A/2)=(cos(A/2))/(sin(A/2))=(sin((A+delta_m)/(2)))/(sin(A/2))`
`sin(90^@-A/2)=sin((A+delta_m)/(2))`
`90^@-A/2=A/2+(delta_m)/(2)impliesdelta_m=180^@-2A`