The refracting angle of a prism is A and refrac tive index of the material of the prism is `cot(A/2)` The angle of minimum deviation is :

Options

A. `pi-A`
B. `pi-2A`
C. `pi-A/2`
D. `pi-4A`

Answer

A, B

Explanation

`eta=(sin((A+delta_m)/(2)))/(sin""A/2)`
`therefore cot A/2=(sin((A+delta_m)/(2)))/(sin""A/2)`
`therefore(cos A//2)/(sin A//2)=(sin((A+delta_m)/(2)))/(sin""A/2)`
`therefore sin(9^@-A/2)=sin((A+delta_m)/(2))`
`therefore (180^@-A)/(2)=(A+delta_m)/(2)`
`therefore 180^@-A=A+delta_m`
`therefore delta_m=180^@-2A` or `delta_m=pi-2A`