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Question
A ray of light falls on a transparent sphere with centre C as shown in the figure. The ray emerges from the sphere parallel to the line AB. Find the angle of refraction at A if the refractive index of the material of the sphere is \[\sqrt{3}\].
Solution
From Snell's law, we have: \[\frac{\sin\left( i \right)}{\sin\left( r \right)} = \mu\] At A, i = 60° (given)
Now, μ = √3
\[\Rightarrow \sin\left( r \right) = \frac{\sin\left( i \right)}{\mu}\]
\[ \Rightarrow \sin\left( r \right) = \frac{\sin\left( 60° \right)}{\sqrt{3}} = \frac{1}{2}\]
\[ \Rightarrow r = \sin^{- 1} \left( \frac{1}{2} \right)\]
\[ \therefore r = 30°\]
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