Question

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 $\sin ^{-1}\left(\begin{array}{ll}\sin & i_{A} \\ \sin & i_{B}\end{array}\right)$

• A. (i) and (iii)
• B. (i) and (iv)
• C. (ii) and (iii)
• D. (ii) and (iv)

Answer 1

Answer: (D)

$i_{B}>i_{A}\Rightarrow $ medium $A$ is denser
$\mu _{A}=\frac{1}{sin i_{A}}$ and $\mu _{B}=\frac{1}{sin i_{B}}$
Also

$ \theta_{C}=\sin ^{-1} \quad\left(\frac{\mu_{B}}{\mu_{A}}\right) $
or $\theta_{C}=\sin ^{-1}\left(\begin{array}{ll}\frac{\sin }{} i_{A} \\ \sin & i_{B}\end{array}\right)$