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 of D line and (b) the angular separation between the C and F lines, given that the refractive indices of the materials are as follows:

Calculate (a) the refracting angle of a flint glass prism which should

1.	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 of D line and (b) the angular separation between the C and F lines, given that the refractive indices of the materials are as follows:
Answer» Solution :Let `A_1 and A_2` be the refracting ANGLES of the flint and crown glass prisms respectively. `mu_1and 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 are 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_2-1)/(mu_1-1))` The negative sign indicates that `A_1 and A_2` are oppositely directed. `A_1/6^@=((1.530-1)/(1.795-1)),A_1=6^@ times 0.530/0.795=-4^@` b) Angular DISPERSION due to the flint glass prism `=A_1(mu_F-mu_C)=-4^@(1.805-1.790)=-0.060` Angular dispersion due to the crown glass prism `=A_2(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.