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

Answer

d.

Explanation

From `sin((A+delta_(m))/(2))=mu "sin"(A)/(2)`
`sin((A+delta_(m))/(2))=("cos"(A)/(2))/("sin"(A)/(2))xx"sin"(A)/(2)`
`(A+delta_(m))/(2)=(pi)/(2)-(A)/(2)`
`delta_(m)=pi-2A=180^(@)-2A`