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 from an achromatic combination of prisms 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^(@)`