Question

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

• A. $\sqrt{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{\sqrt{3}}{2}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

The correct option is D $\frac{1}{\sqrt{3}}$

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

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

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