MCQ
Material $A$ has critical angle $i_A$, and material $B$ has critical angle $i_B\left(i_B>i_A\right)$. 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 $\sin ^{-1}\left(\frac{\sin i_A}{\sin i_B}\right)$
  • A
    (a) (i) and (iii)
  • B
    (b) (i) and (iv)
  • C
    (c) (ii) and (iii)
  • (d) (ii) and (iv)

Answer

Correct option: D.
(d) (ii) and (iv)
(d) We know $C=\sin ^{-1}\left(\frac{1}{\mu}\right)$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$$\begin{aligned}& C_{A B}=\sin ^{-1}\left(\frac{1}{{ }_B \mu_A}\right)=\sin ^{-1}\left[_A \mu_B\right] \\& =\sin ^{-1}\left[\frac{\mu_B}{\mu_A}\right]=\sin ^{-1}\left[\frac{\sin i_A}{\sin i_B}\right]\end{aligned}$

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