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.

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Solution

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 $(ω)$ is given by

$ω = \frac{μ_{v} - u_{r}}{μ_{y} - 1} On substituting the values in the above formula, we get : ω = \frac{(1.68 - 1.56)}{(1.60 - 1)}$
$= \frac{0.12}{0.60} = 0.2$

(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°.

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