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Question
Determine the value of the angle of incidence for a ray of light travelling from a medium of refractive index \[\mu_1 = \sqrt{2}\] into the medium of refractive index \[\mu_2 = 1\] so that it just grazes along the surface of separation.
Solution
The incident ray travelling from denser medium to rarer medium grazes along the surface of the separation of the medium only when the light ray incident at the surface at an angle called critical angle (C) such that the angle of reflection is 90o . Therefore, following Snell's law, we can write
\[\frac{\mu_1}{\mu_2} = \frac{\sin90}{\sin C}\]
\[\frac{\mu_1}{\mu_2} = \frac{1}{\sin C}\]
\[\frac{\sqrt{2}}{1} = \frac{1}{\sin C}\]
\[\sin C = \frac{1}{\sqrt{2}}\]
\[C = \sin^{- 1} (\frac{1}{\sqrt{2}})\]
\[ \therefore \text { Critical angle = Angle of incidence } = {45}^o\]
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