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

Options

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

Answer

A

Explanation

Here, `mu = cot (A//2)`
Acc. To prism formula,
`mu = sin ((A + delta_(m))/(2))/(sin (A//2)) = (cos A//2)/(sin A//2)`
`:. sin ((A + delta_(m))/(2)) = cos A//2 = sn(90^(@) - A//2)`
`(A + delta_(m))/(2) = 90^(@) - A//2`
or `delta_(m) = (180^(@) - 2 A)`