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.

Answer

`- 11.04^(@), -3.12^(@)`

Explanation

`A' = ?, omega' = 0.021, mu' = 1.53`
`A = 4.2^(@), omega = 0.045, mu = 1.65`
For achromatic combination, the condition is
`omegadelta + omega'delta' = 0`
`omega A (mu - 1) + omega'A'(mu' - 1) = 0`
`A' = (- omegaA(mu - 1))/(omega'(mu' - 1)) = (-0.045 xx 4.2 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^(@)`