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Question
Three rays (1, 2, 3) of different colours fall normally on one of the sides of an isosceles right angled prism as shown. The refractive index of prism for these rays is 1.39, 1.47 and 1.52 respectively. Find which of these rays get internally reflected and which get only refracted from AC. Trace the paths of rays. Justify your answer with the help of necessary calculations.
Solution
Critical angle for ray 1:
\[\sin\left( c_1 \right) = \frac{1}{\mu_1} = \frac{1}{1 . 39}\]
\[ \Rightarrow c_1 = \sin^{- 1} \left( \frac{1}{1 . 39} \right) = 46 . 00°\]
Similarly, critical angle of ray 2:
\[\sin\left( c_2 \right) = \frac{1}{\mu_2} = \frac{1}{1 . 47}\]
\[ \Rightarrow c_2 = \sin^{- 1} \left( \frac{1}{1 . 47} \right) = 42 . 86°\]
Similarly, critical angle of ray 3:
\[\sin\left( c_3 \right) = \frac{1}{\mu_3} = \frac{1}{1 . 52}\]
\[ \Rightarrow c_3 = \sin^{- 1} \left( \frac{1}{1 . 52} \right) = 41 . 13°\]
The ray 1 will get totally internally reflected from the side AC with critical equal to 46°. Critical angle of ray 1 is greater than that of i (45°) . Critical angle of ray 2 and 3 is less than that of i. Hence, they will be refracted from the side AC.
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