Question

A certain material has refractive indices 1.56, 1.60 and 1.68  rfor red, yellow and violet lightespectively. (a) Calculate the dispersive power. (b) Find the angular dispersion produced by a thin prism of angle 6° made of this material.

Answer 1

Given:-

Refractive index for red light, μ_r = 1.56

Refractive index for yellow light, μ_y = 1.60

Refractive index for violet light, μ_v = 1.68

Angle of prism, A = 6°

(a)  Dispersive power \[\left( \omega \right)\] is given by

\[\omega = \frac{\mu_v - u_r}{\mu_y - 1}\] 

On substituting the values in the above formula, we get

\[\omega = \frac{\left( 1 . 68 - 1 . 56 \right)}{\left( 1 . 60 - 1 \right)}\]

\[= \frac{0 . 12}{0 . 60} = 0 . 2\]

(b) Angular dispersion = (μ_v − μ_r)A
                                     =(0.12) × 6° = 0.72°

Thus, the angular dispersion produced by the thin prism is 0.72°.