Concept of prism angle

Question:

A thin prism !!P_1!! of angle !!4^0!!, and made from a glass of refractive index !!1.54!!, is combined with another thin prism !!P_2!! made from a glass of refractive index !!1.72,!! to produce dispersion without deviation.

The angle of !!P_2!! is:

(a) !!5.33^0!!

(b) !!4^0!!

(c) !!3^0!!

(d) !!2.6^0!!

Solution

For no deviation !!A_1(mu_1-1) = A_2(mu_2-1)!!

!!A_1 = 4^0, mu_1 = 1.54 and mu_2 = 1.72!!

!!=> 4 (1.54-1)= A_2(1.72-1)!!

!!=> A_2 = (40\ xx0.54)/0.72 = (4xx54)/72= 3^0!!

Therefore, option (c) is correct.