A light ray is incident on a glass slab of thickness 4 3 ~cm and...

A light ray is incident on a glass slab of thickness

4 \sqrt{3} \mathrm{~cm}

and refractive index

\sqrt{2}

. The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass slab is _____

\mathrm{cm}

. \left(\right.

Given \left.\sin 15^{\circ}=0.25\right)

$A light ray is incident on a glass slab of thickness 4 3 ~cm and refractive index 2 . The angle of incidence is equal$

Correct answer

Step-by-step solution

$A light ray is incident on a glass slab of thickness 4 3 ~cm and refractive index 2 . The angle of incidence is equal$

\begin{aligned} & i=\theta_c \\ & \Rightarrow i=\sin ^{-1}\left(\frac{1}{\mu}\right) \\ & \Rightarrow i=45^{\circ} \end{aligned}

and according to snell's law

\begin{aligned} & 1 \sin 45^{\circ}=\sqrt{2} \sin \mathrm{r} \\ & \Rightarrow \mathrm{r}=30^{\circ} \end{aligned}

Lateral displacement

\Delta=\frac{\mathrm{t} \sin (\mathrm{i}-\mathrm{r})}{\cos \mathrm{r}}

\begin{aligned} & \Rightarrow \Delta=\frac{4 \sqrt{3} \times \sin 15^{\circ}}{\cos 30^{\circ}} \\ & \Rightarrow \Delta=2 \mathrm{~cm} \end{aligned}

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