A thin prism is made of a material having refractive indices 1.61 and 1.65 for red and violet light. The dispersive power of the material is 0.07. It is found that a beam of yellow light passing through the prism suffers a minimum deviation of 4.0° in favourable conditions. Calculate the angel of the prism.

Given that, μ base r = 1.61, μ base v = 1.65, ω = 0.07 and δ base y = 4° Now, ω = μ base v - μ base r/ μ base y – 1 ⇒ 0.07 = 1.65 – 1.61/μ base y – 1 ⇒ μ base y – 1 = 0.04/0.07 = 4/7 Again, δ = (μ – 1) A ⇒ A = δ base y/μ base y – 1 = 4/(4/7) = 7°

Sol. Given that, μ base r = 1.61, μ base v = 1.65, ω = 0.07 and δ base y = 4° Now, ω = μ base v - μ base r/ μ base y – 1 ⇒ 0.07 = 1.65 – 1.61/μ base y – 1 ⇒ μ base y – 1 = 0.04/0.07 = 4/7 Again, δ = (μ – 1) A ⇒ A = δ base y/μ base y – 1 = 4/(4/7) = 7°