A thin prism of angle `15^(@)` made of glass of refractive index `mu_(1)=1.5` is combined with another prism of glass of refractive index `mu_(2)=1.75`. The combination of the prism produces dispersion without deviation. The angle of the second prism should be

Options

A. `7^@`
B. `10^@`
C. `12^@`
D. `5^@`

Answer

B

Explanation

Here, `A_1 = 15^ @, mu_1 = 1.5 , mu_2 = 1.75, A_2 = ?`
There will be no deviation for the combination of two prisms of net deviation is zero, i.e.,
`delta_1 + delta_2 = 0`
or `(mu_1 - 1) A_1 + (mu_2 - 1) A_2 = 0`
or `A_2 = -((mu_1 - 1)A_1)/((mu_2 - 1)) = -((1.5 - 1)15^@)/((1.75 - 1)) = - 10^@`
`-ve` sign shows that the second prism is placed in opposition to first prism.