JEE MAIN - Physics (2022 - 27th June Morning Shift - No. 16)
Consider a light ray travelling in air is incident into a medium of refractive index $$\sqrt{2n}$$. The incident angle is twice that of refracting angle. Then, the angle of incidence will be :
$${\sin ^{ - 1}}\left( {\sqrt n } \right)$$
$${\cos ^{ - 1}}\left( {\sqrt {{n \over 2}} } \right)$$
$${\sin ^{ - 1}}\left( {\sqrt {2n} } \right)$$
$$2{\cos ^{ - 1}}\left( {\sqrt {{n \over 2}} } \right)$$
Explanation
According to the law,
$$1 \times \sin \theta = \sqrt {2n} \times \sin \left( {{\theta \over 2}} \right)$$
$$ \Rightarrow \cos {\theta \over 2} = \sqrt {{n \over 2}} $$
$$ \Rightarrow \theta = 2{\cos ^{ - 1}}\left( {\sqrt {{n \over 2}} } \right)$$
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