A thin prism `P_(1)` with angle `4degree` and made from glass of refractive index 1.54 is combined with another thin prism `P_(2)` made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism `P_(2)` is

Options

A. `5.33^(@)`
B. `4^(@)`
C. `3^(@)`
D. `2.6^(@)`

Answer

c.

Explanation

The angle of deviation for the first prism `P_(1), delta_(1)=(mu_(1)-1)A_(1)`.
The angle of deviation for the second prism `P_(2), delta_(2)=(mu_(2)-1)A_(2)`.
Since total deviation is to be zero, therefore
`delta_(1)+delta_(2)=0 rArr (mu_(1)-1)A_(1)+(mu_(2)-1)A_(2)=0`
`A_(2)=((1.54-1))/((1.72-1))4^(@)=3^(@)`
(c) is the correct option.