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

Options

A. `pi + 2A`
B. `pi - 2A`
C. `pi/2 +A`
D. `pi/2 –A`

Answer

B

Explanation

`mu=cot(A/2)`
From snells law,`mu=sin((A+Dm)/2)/(sin(A/2)`
`implies cot(A/2)= cos(A/2)/(sin(A/2))= sin((A+Dm)/2)/(sin(A/2))`
(or)
`sin(90^@ - A/2)= sin((A+Dm)/2)`
`implies90^@-A/2= (A+Dm)/2`
`implies 180^@-A=A+D_(m)`
`therefore D_(m)= 180^@ -2A=pi -2A`