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

Answer: 52

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