Question

A light ray is incident at an angle $45^{\circ}$ with the normal to a $\sqrt{2}\,cm$ thick plate $(\mu = 2)$. Find the shift in the path (in cm) of the light as it emerges out from the plate.

Answer 1

By Snell's law
$\frac{sin\,i}{sin\,r} = \mu$
$\therefore sin\,r = \frac{sin\,i}{\mu} \, ...(i)$

In $\Delta\, ABC,\,\,AC = \frac{AB}{cos\,r}$
In $\Delta\,ACD, \,\, CD = AC \,sin(i - r)$
$ = \frac{AB}{cos\,r}sin(i - r) \,...(ii)$
On substituting $AB = \sqrt{2}\, cm, i = 45^{\circ}$
and solving $CD = 0.62 \,cm$