55. A thin prism of angle 15° made of glass of refractive index $μ_1$ = 1.5 is combined with another prism of glass of refractive index $μ_2$ = 1.75. The combination of the prism produces dispersion without deviation. The angle of the second prism should be ?

55. A thin prism of angle 15° made of glass of refractive index $μ_1$ = 1.5 is combined with another prism of glass of refractive index $μ_2$ = 1.75. The combination of the prism produces dispersion without deviation. The angle of the second prism should be ?

(a) 7°

(b) 10°

(c) 12°

(d) 5°

Answer :  (b) 10°

\( \delta_{min} = - \delta_{min} \)

\( A_1 (\mu_1 - 1) = - A_2 (\mu_2 - 1) \)

\( 15 (1.5 - 1) = - A_2 (1.75 - 1) \)

\( 15 \times 0.5 = - A_2 (0.75) \)

\( 15 \times \frac{2}{3} = - A_2 \)

\( A_2 = -10^\circ \)