A crown glass prism of angle of `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 violet 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 deciation production by the crown prisim is
`delta = (mu-1)A`
and by the flint prism is:
`delta' = (mu' - 1)A`
The prims are placed with their angles inverted with respect to each other. The deviations are also in opposite directions. Thus, the net deviation is:
`D = delta - delta' = (mu -1)A - (mu' -1)A'` ...........(1)
(a) If the net deviation for the mean ray is zero,
`(mu - 1)A = (mu' - 1)A'`
or `A' = ((mu-1))/((mu'-1))A = (1.6-1)/(2.0-1) xx 5^(@) = 3^(@)`
(b) the angular dispersion produced by the crown prism is:
`delta_(V) - delta_(r) = mu_(V0 - mu_(0))A`
and that by the fint prism is,
`delta'_(V) - delta'_(r) = (mu'_(V) - mu'_(t))A`
The net angular dispersion is,
`(mu_(V) - mu_(r))A - (mu'_(V) - mu'_(t))A`
`(1.7 - 1.5) xx 5^(@) - (2.2 - 1.8) xx3^(@)`
The angular dispertion has magnitude `0.2^(@)`