Question

A ray of light incident parallel to the base PQ of an isosceles right-angled triangular prism PQR suffers two successive total internal reflections at the faces PQ and QR before reversed in direction as shown. If the refractive index of the material of the prism is $\mu$, then find the value of $\mu$.

Answer 1

Total internal reflection condition

$45°+r>C$

and $45°-r>C$

or $90°>2C$

and $\mu \times \sin C=1\times \sin 90°$

$\therefore \mu =\frac{1}{\sin C}$

hence $45°>C$

or $\sin 45°>\sin C\frac{1}{\sqrt{2}}>\frac{1}{\mu }\therefore \mu >\sqrt{2}$