The dispersive powers of crown and flint glasses are `0.03` and `0.05` respectively. The refractive indices for yellow light for these glasses are `1.517` and `1.621` respectively. It is desired to form an achromatic combination of prism of crown and flint glasses which can produce a deviation of `1^@` in the yellow ray. Find the refracting angles of the two prisms needed.

Explanation

Crown glass: `omega=0.03`, `mu_y=1.517`
Flint glass: `omega^'=0.05`, `mu_y^'=1.621`
For no dispersion:
`(mu_v-mu_r)A=(mu_v^'-mu_r^')A^'`
`omega(mu_y-1)A=omega^'(mu_y^'-1)A^'`
`[omega=(mu_v-mu_r)/(mu_y-1)`, `omega^'=(mu_v^'-mu_r^')/(mu_y^'-1)]'`
`0.03(1.517-1)A=0.05(1.621-1)A^'`
Deviation
`delta_0=|(mu_y-1)A-(mu_y^'-1)A^'|`
`1=|(1.517-1)A-(1.621-1)A^'|`
`=|0.517A-0.621A^'|=|0.517xx2A^'-0.621A^'|`
`1=0.413A^'impliesA^'=2.42^@`
`A=2A^'=4.84^@`