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

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)=(cosA//2)/(sinA//2)`
Here
`sin((A+delta_(M))/(2)) = cos((A)/(2)) =sin((pi)/(2)-(A)/(2))`
then `(A+delta m)/(2)=(pi)/(2)-(A)/(2) rArr delta = pi -2A`
or `delta =180^(@) -2A`