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

`omega_(C) = 0.03 = (n_(v) - n_(t))/(n_(y) - 1)`
`:. (n_(V) - n_(t)) = 0.03 (1.517-1) = 0.0155`
and, `omega_(f) = 0.05 = (n'_(v) - n'_(f))/(n_(y)-1)`
`:. M'_(v) - mn'_(f) = 0.05 xx (1.621-1) = 0.031`
`theta = (n_(v) - n_(r))A - (n'_(v) - n'_(f))A'`
`= 0.0155A - 0.031 A' ....(1)`
But `deleta_("net") = 1`
So, `(n_(Y) - 1)A - n'_(y) - 1)A' = 1`
`= 0.517A - 0.621A' = 1.....(2)`
`:. A = 4.8^(@)` and `A' = 2.4^(@)`