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?
(A) Light can be totally internally reflected when it passes from B to A
(B) Light can be totally internally reflected when it passes from A to B
(C) Critical angle between A and B is $(i_B–i_A)$
(D) Critical angle between A and B is ${\sin }^{-1}\left(\frac{\sin i_A}{\sin i_B}\right)$

• A. (A) and (C)
• B. (A) and (D)
• C. (B) and (C)
• D. (B) and (D)

Answer 1

The correct option is D (B) and (D)

For critical angle $\left({\theta }_c\right)$,
$\sin {\theta }_c=\frac{1}{\mu }$
Now, $i_A<i_B$ (Given)
$\frac{1}{{\mu }_A}<\frac{1}{{\mu }_B}$
$\sin i_A=\frac{1}{{\mu }_A},\sin i_B=\frac{1}{{\mu }_B}$
${\mu }_B<{\mu }_A$
Thus, material A is optically denser than material B.
Hence, light can be totally internally reflected when it passes from material A to B.
Let critical angle between A to B be ${\theta }_c$.
$\sin {\theta }_c=\frac{{\mu }_B}{{\mu }_A}{\theta }_c={\sin }^{-1}\frac{\sin i_A}{\sin i_B}$
Hence, the correct answer is option (d).