A thin prism with angle $5^{\circ}$ of refractive index 1.72 is combined with another prism of refra

Question

A thin prism with angle $5^{\circ}$ of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of second prism is $\_\_\_\_$ .

Professor PC Thomas Classes · Answer

For a combination of two thin prisms to produce dispersion without deviation, the net deviation must be zero. The deviation produced by a thin prism is $\delta = A(\mu - 1)$. For zero net deviation, their deviations must be equal and opposite: $A_1(\mu_1 - 1) = A_2(\mu_2 - 1)$. Substituting the given values: $5^\circ (1.72 - 1) = A_2 (1.9 - 1) \implies 5^\circ(0.72) = A_2(0.90) \implies 3.6 = 0.9 A_2 \implies A_2 = \frac{3.6}{0.9} = 4^\circ$.