Physics - Geometrical Optics Question with Solution | TestHub

From the given figure, the light ray X is incident normally on the face PQ of the right-angled isosceles prism.

It passes undeviated through face PQ and strikes the face PR.

From the geometry of the prism, the normal to the face PR makes an angle of $45^{\circ }$ with the horizontal. Thus, the angle of incidence at the face PR is $i=45^{\circ }$.

The diagram shows the ray undergoing total internal reflection at the face PR to emerge as ray Y.

For total internal reflection to occur, the angle of incidence must be greater than or equal to the critical angle $C$.

$i\ge C$

$\sin 45^{\circ }\ge \sin C$

Using the relation $\sin C=\frac{1}{\mu }$, where $\mu$ is the refractive index of the material of the prism:

$\frac{1}{\sqrt{2}}\ge \frac{1}{\mu }$

$\mu \ge \sqrt{2}$

The minimum refractive index required for this phenomenon is $\sqrt{2}$.

Answer: $\sqrt{2}$