A small angled prism of refractive index 1.4 is combined with another small angled prism of refractive index 1.6 to produce disperison without deviation. If the angle of first prism is `6(@)`, then the angle of the second prism is

Options

A. `8^(@)`
B. `6^(@)`
C. `4^(@)`
D. `2^(@)`

Answer

C

Explanation

We know about the thin prism, `delta_(m)=(mu-1)A`
In given condition, `A_(1)(mu_(1)-1)A_(2)(mu_(2)-1)`
Given, `mu_(1)=1.4, mu_(2)=1.6 and A_(1)=6^(@)`
`"Now", 6(1.4-1)=A_(2)(1.6-1)`
`A_(2)=(6xx0.4)/(0.6) Rightarrow A_(2)=(2.4)/(0.6)`
`A_(2)=4^(@)`
Hence, the angle of the second prism is `4^(@)`.