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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.
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Solution
Given:-
Refractive index for red light, μr = 1.56
Refractive index for yellow light, μy = 1.60
Refractive index for violet light, μv = 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 = (μv − μr)A
=(0.12) × 6° = 0.72°
Thus, the angular dispersion produced by the thin prism is 0.72°.
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