Consider an equilateral prism (refractive index $\sqrt{2}$ ). A ray of light is incident on its one

Question

Consider an equilateral prism (refractive index $\sqrt{2}$ ). A ray of light is incident on its one surface at a certain angle $i$. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to $\_\_\_\_$

Professor PC Thomas Classes · Answer

For an equilateral prism, $A = 60^\circ$. Since the emergent ray grazes the second surface, the angle of emergence is $e = 90^\circ$. This implies the ray hits the second surface at the critical angle, so $r_2 = \sin^{-1}(\frac{1}{\mu}) = \sin^{-1}(\frac{1}{\sqrt{2}}) = 45^\circ$. From the geometry of the prism, the sum of the internal angles of refraction is $r_1 + r_2 = A$. Thus, $r_1 + 45^\circ = 60^\circ$, which gives the angle of refraction at the incident surface as $r_1 = 15^\circ$.