Optics Question 944
Question: A ray of light passes from vacuum into a medium of refractive index $ \mu , $ the angle of incidence is found to be twice the angle of refraction. Then the angle of incidence is
Options:
A) $ {{\cos }^{-1}}(\mu /2) $
B) $ 2{{\cos }^{-1}}(\mu /2) $
C) $ 2{{\sin }^{-1}}(\mu ) $
D) $ 2{{\sin }^{-1}}(\mu /2) $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] By using $ \mu =\frac{\sin i}{\sin r} $
$ \Rightarrow $ $ \mu =\frac{\sin 2r}{\sin r}=\frac{2\sin r\cos r}{\sin r} $ $ (\sin 2\theta =2\sin \theta \cos \theta ) $
$ \Rightarrow $ $ r={{\cos }^{-1}}( \frac{\mu }{2} ) $ So, $ i=2r={{\cos }^{-1}}( \frac{\mu }{2} ) $
