Question

A ray of light travels from water to air as shown below. Given that the refractive index of air is $1.0$ and the refractive index of water is $1.3$, what is the angle of incidence$\left(i\right)$?

• A. ${\sin }^{-1}\left(\frac{5}{13}\right)$
• B. ${\sin }^{-1}\left(\frac{5}{11}\right)$
• C. ${\sin }^{-1}\left(\frac{5}{17}\right)$
• D. ${\sin }^{-1}\left(\frac{5}{19}\right)$

Answer 1

The correct option is A ${\sin }^{-1}\left(\frac{5}{13}\right)$


From Snell's law,
$n_1\sin i=n_2\sin r$

Here, $n_1=1.3$ and $n_2=1.0$

So, $1.3\sin i=1\sin {30}^{\circ }$

$\Rightarrow \frac{13}{10}\sin i=\frac{1}{2}$

$\Rightarrow \sin i=\frac{5}{13}$

$\therefore i={\sin }^{-1}\left(\frac{5}{13}\right)$

Why this question? By this question, we can understand the application of Snell's law.