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}} ] $



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