Question

Find the value of $\sin {\theta }_1$ in the diagram given below.
Given: $n_{glass}=1.5$ and $n_{air}=1$

Answer 1

Using snell's law at the first boundary: (Air to water )
$n_{air}\sin {\theta }_{air}=n_{water}\sin \theta ...\left(i\right)$

Inside the glass refracted ray from first refraction is the incident ray for the second refraction. And this ray makes alternate interior angles with both the interface. So both the angles will be equals. Which is represented by $\theta$ here:

Using snell's law at the second boundary: ( Water to air )
$n_{water}\sin \theta =n_{glass}\sin {\theta }_1...\left(ii\right)$

Equating (i) and (ii),
$n_{air}\sin {\theta }_{air}=n_{glass}\sin {\theta }_1$
$1\times \frac{\sqrt{3}}{2}=1.5\times \sin {\theta }_1$
$\sin {\theta }_1=\frac{1}{\sqrt{3}}$

So, the value of $\sin {\theta }_1=\frac{1}{\sqrt{3}}$