A crown glass prism of angle `5^@` is to be combined with a flint glass prism in such a way that the mean ray passes undeviated. Find (a) the angle of the flint glass prism needed and (b) the angular dispersion produced by the combination when white light goes through it. Refractive indices for red, yellow and viloet light are 1.514, 1.517 and 1.523 respectively for crown glass and 1.613 1.620 and 1.632 for flint glass.

Explanation

The deviation produced by the crown prism is
`delta = (mu - 1)A`
and by the flint prism is `delta' = (mu' - 1)A'`
The prisms are placed with respect to each other. The deviation are also in opposite direction. Thus, the net deviation is
`D = delta -delta' = (mu-1)A - (mu' - 1)A'.... (i)`
(a) if the net deviation for the mean ray is zero,
`(mu -1)A = (mu' -1)A'`
or `A' = ((mu -1)/((mu' -1))A = (1.517-1)/(1.620 -1)xx5^@`
`=4.2^@`
(b) The angular dispersion prouced by the crown prism is
`delta_(upsilon) - delta_r= (mu_(upsilon) - mu_r)A`
and that by the fint prism is
`delta_(upsilon) - delta_r = (mu_(upsilon) - mu_r)A'`
The net angular dispersion is,
`delta = (mu_(upsilon) - mu_r)A - (mu_(upsilon) - mu_r)A'`
`=(1.523 - 1.514 xx 5^@ - (1.632 - 1.613) xx 4.2^@`
`=- 0.-348^@.`
The angular dispersiom has magnitude `0.0348^@.`