A ray of light is incident from air on a glass plate having...

Let $C$ be the critical angle.

Then, $sinC = \dfrac{1}{\mu}$, where, $\mu$ is the refractive index of glass.

So, $sinC = \dfrac{1}{\sqrt{2}} ⇒$$C = 45 °$

As the angle of incidence is equal to the critical angle, so using Snell's law,

$sinC = \mu sin\theta$

$⇒ \dfrac{1}{\sqrt{2}} = \sqrt{2}sin\theta$

$⇒ \theta = 30 °$

Now, lateral displacement of the ray is

$x = tsin ( i - r ) secr$

$⇒ x = \sqrt{3}\sin \left(45 ° - 30 °\right)\sec 30 °$

$⇒ x = \sqrt{3} ( 0 . 26 ) \left(\dfrac{2}{\sqrt{3}}\right)$

$⇒ x = 0 . 52cm$

$⇒ x = 52 \times {10}^{- 2}cm$