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Three thin prisms are combined as shown ...

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.

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The correct Answer is:
A, B
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))`
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