Optics Question 984
Question: Glass has refractive index m with respect to air and the critical angle for a ray of light going from glass to air is q. If a ray of light is incident from air on the glass with angle of incidence q, the corresponding angle of refraction is
[MP PMT 2004]
Options:
A) $ {{\sin }^{-1}}( \frac{1}{\sqrt{\mu }} ) $
B) $ 90^{o} $
C) $ {{\sin }^{-1}}( \frac{1}{{{\mu }^{2}}} ) $
D) $ {{\sin }^{-1}}( \frac{1}{\mu } ) $
Show Answer
Answer:
Correct Answer: C
Solution:
$ _{a}{\mu _{g}}=\frac{1}{\sin \theta } $
$ \Rightarrow \mu =\frac{1}{\sin \theta } $ …..(i) Now from Snell’s law $ \mu =\frac{\sin i}{\sin r} $
$ =\frac{\sin \theta }{\sin r} $
$ \Rightarrow \sin r=\frac{\sin \theta }{\mu } $ …..(ii) From equation (i) and (ii) $ \sin r=\frac{1}{{{\mu }^{2}}} $
$ \Rightarrow r={{\sin }^{-1}}( \frac{1}{{{\mu }^{2}}} ) $
