Physics - Wave Optics Question with Solution | TestHub

According to Brewster's law, when a ray of light is incident at Brewster's angle $\Phi$, the refractive index of the medium is given by $\mu =\tan \Phi$.

By Snell's law, $\mu =\frac{\sin \Phi }{\sin r}$, where $r$ is the angle of refraction.

Equating the two expressions for $\mu$, we get:

$\frac{\sin \Phi }{\cos \Phi }=\frac{\sin \Phi }{\sin r}$

$\sin r=\cos \Phi =\sin (90^{\circ }-\Phi )$

$\Rightarrow r=90^{\circ }-\Phi$

The angle of reflection is equal to the angle of incidence, so the angle of reflection is $\Phi$.

The angle between the reflected and refracted rays is $180^{\circ }-(\Phi +r)$.

Substituting the value of $r$, we get:

$180^{\circ }-(\Phi +90^{\circ }-\Phi )=90^{\circ }$

Thus, the reflected and refracted rays are mutually perpendicular.

Answer: $90^{\circ }$