A thin prism P of refracting angle `3^@ and ` refractive index 1.5 combined with another thin prism Q of refractive index 1.6 to produce dispersion without deviation. Then the angle of prism Q is

Options

A. `3^@`
B. `4^@`
C. `3.5^@`
D. `2.5^@`

Answer

D

Explanation

Given refracting angle of prism P
`A_p=3^@`
and refractive index of prism P
`mu_p=1.5`
and refractive index of prism Q
`mu_Q=1.6`
`(mu_p-1) A_p=(mu_Q-1)A_Q`
`(1.5-1)3^@=(1.6-1)A_Q`
or `0.5 times 3=0.6 times A_Q`
or `A_Q=(0.5 times 3)/0.6`
or `A_Q=2.5^@`