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

Answer

C

Explanation

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