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Question
The minimum deviations suffered by, yellow and violet beams passing through an equilateral transparent prism are 38.4°, 38.7° and 39.2° respectively. Calculate the dispersive power of the medium.
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Solution
Given:-
Minimum deviations suffered by
Red beam, δr = 38.4°
Yellow beam, δy = 38.7°
Violet beam, δv = 39.2°
If A is the angle of prism having refractive index μ, then the angle of minimum deviation is given by
\[\delta = (\mu - 1)A\]
\[\therefore\left( \mu - 1 \right) = \frac{\delta}{A}.........(1)\]
Dispersive power \[\left( \omega \right)\] is given by
\[\omega = \frac{\mu_v - \mu_r}{\mu_y - 1}\]
\[ = \frac{( \mu_v - 1) - ( \mu_r - 1)}{( \mu_y - 1)}\]
From equation (1), we get
\[\omega = \frac{\frac{\delta_v}{A} - \frac{\delta_r}{A}}{\frac{\delta_y}{A}}\]
\[\Rightarrow \omega = \frac{\delta_v - \delta_r}{\delta_y} = \frac{(39 . 2) - (38 . 4)}{(38 . 7)}\]
\[\Rightarrow \omega = \frac{(0 . 8)}{38 . 7} = 0 . 0206\]
So, the dispersive power of the medium is 0.0206.
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