Question

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 angle of the prism.

Answer 1

The refractive indices for red and yellow lights are μ_r = 1.61 and μ_y = 1.65, respectively.

Dispersive power, ω = 0.07

Angle of minimum deviation, δ_y = 4°

Now, using the relation \[\omega = \frac{\mu_v - \mu_r}{\mu_y - 1},\] we  get

\[ \Rightarrow 0 . 07 = \frac{1 . 65 - 1 . 61}{\mu_y - 1}\]

\[\Rightarrow  \mu_y  - 1 = \frac{0 . 04}{0 . 07} = \frac{4}{7}\]

Let the angle of the prism be A.

Angle of minimum deviation, δ = (μ − 1)A

\[\Rightarrow A = \frac{\delta_y}{\mu_y - 1} = \frac{4}{\left( \frac{4}{7} \right)} = 7^\circ\]

Thus, the angle of the prism is 7°.