NEET 2020 Physics Question 138 Solution

When unpolarized light is incident on the interface separating two media, the reflected light is completely plane-polarized when the angle of incidence equals Brewster's angle ($$i_b$$), where reflected and refracted rays are mutually perpendicular ($$i_b + r = 90^\circ$$).

Using Snell's law with $$r = 90^\circ - i_b$$: $$\frac{\sin i_b}{\sin r} = \mu \implies \frac{\sin i_b}{\sin(90^\circ - i_b)} = \frac{\sin i_b}{\cos i_b} = \tan i_b = \mu$$

For any transparent optical medium (e.g. water $$\mu = 1.33$$, glass $$\mu = 1.5$$, diamond $$\mu = 2.42$$) surrounded by air/vacuum ($$\mu_{\text{air}} = 1$$): $$\mu > 1$$ And for any real physical material, refractive index is finite: $$1 < \mu < \infty$$

Because the tangent function is strictly monotonically increasing in the first quadrant ($$0^\circ < i_b < 90^\circ$$): $$\tan(45^\circ) = 1 \quad \text{and} \quad \tan(90^\circ) = \infty$$ $$1 < \tan i_b < \infty \implies 45^\circ < i_b < 90^\circ$$ This confirms Option (3).