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

Answer

D

Explanation

As `mu=(sin((A+delta)/(2)))/(sin((A)/(2)))`
`cot.(A)/(2)=(sin.((A+delta)/(2)))/(sin.((A)/(2)))[ :.mu=cot.(A)/(2)]`
`(cos((A)/(2)))/(sin((A)/(2)))=(sin.((A+delta)/(2)))/(sin((A)/(2)))impliessin((pi)/(2)-(A)/(2))=sin((A)/(2)+(delta)/(2))`
`(pi)/(2)-(A)/(2)=(A)/(2)+(delta)/(2)`
`:.delta=pi-2A=180^(@)-2A`