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  2. Question
  3. Physics
  4. A ray of light travelling in a denser medium strikes the boundary of a rarer medium. The ray gets partially reflected and refracted. The angle of reflection is r and that of refraction is r' . If the reflected and refracted rays make an angle of 90° with each other then the critical angle for the pair of media is

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Q. A ray of light travelling in a denser medium strikes the boundary of a rarer medium. The ray gets partially reflected and refracted. The angle of reflection is $r$ and that of refraction is $r^{'}$ . If the reflected and refracted rays make an angle of $90^\circ $ with each other then the critical angle for the pair of media is

NTA AbhyasNTA Abhyas 2020Ray Optics and Optical Instruments

Solution:

Solution
$D \mu_R=\frac{\sin r}{\sin r^{\prime}}$ -----(1)
from equation (1) & (2)
$\sin C=\frac{\sin r}{\sin (90-r)} \Rightarrow \sin r=\tan r \Rightarrow C=\sin ^{-1} \tan r$