Optics Question 985
Question: Material A has critical angle $ i _{A}, $ and material B has critical angle $ i _{B}(i _{B}>i _{A}). $ Then which of the following is true (i) Light can be totally internally reflected when it passes from B to A (ii) Light can be totally internally reflected when it passes from A to B (iii) Critical angle for total internal reflection is $ i _{B}-i _{A} $ (iv) Critical angle between A and B is $ {{\sin }^{-1}}( \frac{\sin i _{A}}{\sin i _{B}} ) $
[UPSEAT 2004]
Options:
A) (i) and (iii)
B) (i) and (iv)
C) (ii) and (iii)
D) (ii) and (iv)
Show Answer
Answer:
Correct Answer: D
Solution:
We know $ C={{\sin }^{-1}}( \frac{1}{\mu } ) $ .
Given critical angle $ i _{B}>i _{A} $ .
So $ {\mu _{B}}<{\mu _{A}} $ i.e. B is rarer and A is denser.
Hence light can be totally internally reflected when it passes from A to B
Now critical angle for A to B $ C _{AB}={{\sin }^{-1}}( \frac{1}{ _{B}{\mu _{A}}} ) $
$ ={{\sin }^{-1}}[ _{A}{\mu _{B}} ] $
$ ={{\sin }^{-1}}[ \frac{{\mu _{B}}}{{\mu _{A}}} ] $
$ ={{\sin }^{-1}}[ \frac{\sin i _{A}}{\sin i _{B}} ] $
