Calculate (a) the refracting angle of a flint glass prism which should be combined with a crown glass prism of refracting angle 6° so that the combination may have no deviation for D line and (b) the angular separation between the C and F lines, given that the refractive indices of the materials are as follows:

Explanation

Let `A_1` and `A_2` be the refracting angles of the flint and crown glass prisms respectively. `mu_1 ` and `mu_2` be the refractive indices for the D line of flint and crown glasses respectively. (a) If `delta_1 , and delta_2`, be the angles of deviations due to the flint and crown glass prisms respectively, then for no deviation of D line
` delta _1 +delta _2 =0 , A_1 ( mu_1 -1) + A_2 (mu_2 -1) =0`
` (A_1)/(A_2)=- ((mu_1-1)/(mu_1))`
The negative sign indicates that `A_1` and `A_2` are oppositely directed.
` (A_1 )/(6^0 ) = ((1.530 -1)/(1.795 -1)) , A_1 = 6^0 xx (0.530 )/( 0.795 )=-4^@ `

(b) Angular dispersion due to the flint glass prism
`=A_1 (mu_F - mu_C )_2 = 6^@ ( 1.535 - 1.527 ) = 0.048 `
Net angular dispersion = 0.048 -0.060 = -0.012 The negative sign indicates that the resultant dispersion is in the direction of the deviation produced by the flint prism.