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

Options

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

Answer

A

Explanation

`n = (sin ((A + delta_(m))/(2) ))/(sin A//2)`
`rArr " " cot((A)/(2)) = (sin ( (A + delta_(m))/(2) ) )/(sin (A//2))`
`rArr " " (cos(A//2))/(sin (A//2)) = (sin ((A + delta_(m))/(2)))/(sin (A//2))`
`rArr " " sin ((A + delta_(m))/(2)) = sin (90^(@) - A//2)`
`rArr (A)/(2) + (delta_(m))/(2) = 90^(@) - A//2 `
`rArr " " delta_(m) = 180^(@) - 24`A.