Three thin prisms are combined as shown in figure. The refractive indices of the crown glass for red, yellow and violet rays are `mu_r, mu_y and mu_v` respectively and those for the flint glass are `mu_r^', mu_y^' and mu_v^'` respectively. Find the ratio A'/A for which (a) there is no net angular dispersion, and (b) there is no net deviation in the yellow ray.

Answer

A, B

Explanation

Total deviation for yellow ray produced by the prismcombination is ,
`delta_y = delta_(ey) - delta_(ty)`
` =2 delta_(ey) - 2delta_(ry)`
`= 2 (mu_y + 1)A - (mu_(re) -1)A`
Similarlyu the angular dispersion produced by the combination is
`(a) For net angular dispersion to be zero,
`delta_t - delta_t = 0 =2 (mu_(upsilon c) - mu_(tc)A`
`=(mu_(upsilon t) - mu_(rt)A`
rArr (A)/(A) = (2(mu_(upsilon c) - mu_(r c)`/((mu_(upsilon c) - uu_rc)`
`= (2(mu_r - u_r))/((mu_r - mu))`
(b) Fro net deviation in the yellow ray to be zero,
`delta = -0`
`rArr 2(mu_(cy) -1)A = (2(mu_(cy) -1))/((mu_(ty) -1))`
`=(2(mu_y -1))/((mu_y -1))`