Question 104 of 295

A ray of light is incident at an angle of incidence $60^{\circ}$ on the glass slab of refractive index $\sqrt{3}$. After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is $4\sqrt{3}cm$. The thickness of the glass slab is _____ $cm$.

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Answer: 12

From snell's law, $\dfrac{\sin i}{\sin r}=\sqrt{3}\Rightarrow \dfrac{\sin 60^{\circ}}{\sin r}=\sqrt{3}\Rightarrow r=30^{\circ}$
From the diagram shown, $d=\dfrac{t\sin \left(i-r\right)}{\cos r}\Rightarrow \dfrac{t\times \dfrac{1}{2}}{\dfrac{\sqrt{3}}{2}}=4\sqrt{3}\Rightarrow t=12cm$