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

Crown glass: `mu_r=1.514`, `mu_y=1.517`, `mu_v=1.523`, `A=5^@`
Flint glass: `mu_r^'=1.613`, `mu_y^'=1.620`, `mu_v^'=1.632`, `A^'=?`
(a) For no deviation:
`(mu_y-1)A=(mu_y^'-1)A^'`
`(1.517-1)xx5=(1.620-1)A^'`
`A^'=4.17^@`
(b) Angular dispersion
`theta_0=theta_1-theta_2=|(mu_v-mu_r)A-(mu_v^'-mu_r^')A|`
`=|(1.523-1.514)xx5-(1.632-1.613)xx4.17|`
`=|0.045-0.079|`
`=0.034^@`