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

Answer

A

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/2+(delta_(m))/2)`
`90^(@)-A/2=A/2+(delta_(m))/2`
`delta_(m)=180^(@)-2A`