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

Answer

A, B

Explanation

`mu=(sin((delta_m+A)/(2)))/(sin""A/2)`
`cot A/2=(sin((delta_m+A)/(2)))/(sin""A/2)`
`(cos""A/2)/(sin""A/2)=(sin((delta_m+A)/(2)))/(sin""A/2)`
`cos""A/2=sin((delta_m+A)/(2))`
`therefore sin(90^@-A/2)=sin((delta_m+A)/(2))`
`therefore 90^@-A/2=(delta_m+A)/(2)`
`therefore 180^@-A=delta_m+A`
`therefore 180^@-2A=delta_m`
`therefore delta_m=180^@-2A`