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

Options

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

Answer

D

Explanation

`cot.(A)/(2) = (sin((delta_("min)+A)/(2)))/(sin((A)/(2)))`
`cos.(A)/(2) = sin ((delta_("min")+A)/(2))`
`sin((pi)/(2)-(A)/(2)) = sin ((delta_("min")+A)/(2))`
`rArr (pi)/(2)-(A)/(2) = (delta_("min"))/(2)+(A)/(2)`
`= (pi)/(2)-A = (delta_("min"))/(2)`
`Delta_("min") = pi - 2A`