Question

Light travels in two media $M_1$ and $M_2$ with speeds $1.5\times 10^{8}m{s}^{-1}$ and $2.0\times 10^{8}m{s}^{-1}$ respectively. The critical angle between them is:

• A. ${\tan }^{-1}\left(\frac{3}{\sqrt{7}}\right)$
• B. ${\tan }^{-1}\left(\frac{2}{3}\right)$
• C. ${\cos }^{-1}\left(\frac{3}{4}\right)$
• D. ${\sin }^{-1}\left(\frac{2}{3}\right)$

Answer 1

Answer: (A)

$v=\frac{c}{n}$
$n_d\sin i_c=n_r\sin 90^{\circ }$
$\sin i_c=\frac{n_r}{n_d}=\frac{v_d}{v_r}$
$\sin i_c=\frac{1.5\times 10^8}{2\times 10^8}=\frac{1.5}{2}$
$\sin i_c=\frac{3}{4}$
$\tan i_c=\frac{3}{\sqrt{4^2-3^2}}\Rightarrow \frac{3}{\sqrt{7}}$
$i_c={\tan }^{-1}\left(\frac{3}{\sqrt{7}}\right)$