A prism is made up of material of refractive index `sqrt3`. The angle of prism is `A`. If the angle of minimum deviation is equal to the angle of the prism, then the value of A is

Options

A. `sin^(-1)((mu)/(2))`
B. `sin^(-1)(sqrt((mu-1)/(2)))`
C. `2cos^(-1)((mu)/(2))`
D. `cos^(-1)((mu)/(2))`

Answer

C

Explanation

`mu=(sin((A+delta_(m))/(2)))/(sin((A)/(2)))`
Here, `delta_(m)=A`
`:.mu=(sinA)/(sin((A)/(2)))=(2sin((A)/(2))cos((A)/(2)))/(sin((A)/(2)))=2cos((A)/(2))`
`A=2cos^(-1)((mu)/(2))`