Calculate the angle of a prism of dispersive power `0.021` and refractive index `1.53` to form an achromatic combination with prism of angle `4.2^@`, and dispersive power `0.045`, having refractive index `1.65`. Find also the net deviation.

Options

A. ` -7.08^@`, `-4.66^@`
B. ` -11.04^@`, `-3.12^@`
C. ` -11.04^@`, `-6.02^@`
D. ` -6.08^@`, `-1.21^@`

Answer

B

Explanation

`A' = ?, omega' = 0.021, mu' = 1.53`
`A = 4.2^@, omega = 0.045, mu = 1.65`
For achromatic combination, the condition is
`omega delta + omega' delta' = 0`
`omega A (mu - 1) + omega' A' (mu' - 1) = 0`
`A' = (-omega A(mu - 1))/(omega' (mu' - 1)) =(-0.045 xx4.2 xx 0.65)/(0.021 xx 0.53)`
`A' = -11.04^@`
Net deviation `=(mu - 1) A + (mu' - 1) A'`
=`(1.65 - 1)(4.2)+(1.53 - 1)(-11.04)`
=`- 3.12^@`.