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Question
A flint glass prism and a crown glass prism are to be combined in such a way that the deviation of the mean ray is zero. The refractive index of flint and crown glasses for the mean ray are 1.620 and 1.518 respectively. If the refracting angle of the flint prism is 6.0°, what would be the refracting angle of the crown prism?
Solution
Given:-
Refractive index of the flint glass, μf = 1.620
Refractive index of the crown glass, μc = 1.518
Refractive angle of the flint prism, Af = 6°
Now,
Let the refractive angle of the crown prism be Ac.
For the net deviation of the mean ray to be zero,
Deviation by the flint prism = Deviation by the crown prism
i.e., (μf − 1)Af = (μc − 1)Ae
\[\Rightarrow A_c = \left( \frac{\mu_f - 1}{\mu_e - 1} \right) A_f\]
\[\Rightarrow A_c = \left( \frac{1 . 620 - 1}{1 . 518 - 1} \right) \times 6 . 0^\circ = 7 . 2^\circ\]
Thus, the refracting angle of the crown prism is 7.2°.
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