Question

Trace the path of a ray of light incident at an angle of 45° on a rectangular glass slab. Write the measure of the angle of refraction, the angle of emergence and the lateral displacement suffered by the ray as it passes through the slab. 

Answer 1

In the figure, angle i is he angle of incidence, angle r is the angle of refraction and angle e is the angle of emergence.

Using snell's law, angle of refraction can be found out as follows:
\[\frac{\sin i}{\sin r} = \frac{\mu_2}{\mu_1} = \frac{1 . 5}{1}\]

\[\sin r = \sin i \times \frac{10}{15}\]

\[since, \angle i = {45}^o (\text{given})\]

\[\sin r = \sin {45}^o \times \frac{10}{15}\]

\[\sin r = \frac{1}{\sqrt{2}} \times \frac{2}{3}\]

\[r = 28 . {13}^o \]
and we know
\[\angle e = \angle i\]
\[ \Rightarrow \angle e = {45}^o\]
Note: We cannot measure lateral displacement suffered by the ray because to calculate it we should know the thickness of the glass slab as formula to calculate lateral displacement is
\[\text{Lateral displacement }= \frac{t \sin(i - r)}{\cos r}\]
where, t = thickness of the glass slab.

But thickness of the slab is not mentioned in the question.