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^r 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.

Three thin prisms are combined as shown in figure. The refractive indi

1.	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^r 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» Solution :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` Similarlyuthe 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))`

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