The Brewster's angle $i_p$ for an unpolarised beam of light traveling from a optically denser medium

Question

The Brewster's angle $i_p$ for an unpolarised beam of light traveling from a optically denser medium to a rarer medium (where the relative refractive index of the second medium with respect to the first is $\mu_r < 1$) must strictly lie in the mathematical range

Professor PC Thomas Classes · Answer

(a) : Brewster's angle is determined by the fundamental relation $	an i_p = \mu_r$. When light travels from an optically denser medium to a rarer medium, the relative refractive index $\mu_r$ is strictly less than 1 ($0 < \mu_r < 1$). Since the tangent function increases monotonically from $	an(0^{\circ}) = 0$ to $	an(45^{\circ}) = 1$, the corresponding Brewster's angle $i_p$ must definitively lie in the restricted range $0^{\circ} < i_p < 45^{\circ}$.