Question

A ray of light is incident from air on a glass plate having thickness $\sqrt{3} cm$ and refractive index $\sqrt{2}$. The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is ___$\times 10^{-2} cm$. (given $\sin 15^{\circ}=0.26$ )

Answer 1

$ \sin c =\frac{1}{\sqrt{2}}$
$ c =45^{\circ}$
$\sin c =\mu \sin \theta$
$\frac{1}{\sqrt{2}}=\sqrt{2} \sin \theta$
$ \theta=30^{\circ}$
Lateral displacement:
$ x=t \sin (i-r) \sec r$
$x=\sqrt{3} \sin \left(45^{\circ}-30^{\circ}\right) \sec 30^{\circ}$
$ x=\sqrt{3}(0.26)\left(\frac{2}{\sqrt{3}}\right) $
$ X=0.52\, cm $
$x=52 \times 10^{-2} cm$