When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of refracted
beam with respect to the normal is ______ .

($$\tan^{-1}$$ (1.52) = $$57.7^{o}$$, refractive indices of air and glass are 1.00 and 1.52, respectively.)

We need to find the angle of refraction when unpolarized light falls on a glass plate at Brewster's angle.

According to Brewster's law, when unpolarized light strikes a surface at Brewster's angle, the reflected light is completely linearly polarized and satisfies $$\tan \theta_B = \frac{\mu_2}{\mu_1}$$, where $$\theta_B$$ is Brewster's angle, $$\mu_2$$ is the refractive index of the glass, and $$\mu_1$$ is the refractive index of air.

An important feature at Brewster's angle is that the reflected ray and the refracted ray are perpendicular, so $$\theta_B + \theta_r = 90°$$, with $$\theta_r$$ denoting the angle of refraction.

First, we calculate Brewster's angle by evaluating $$\theta_B = \tan^{-1}\left(\frac{1.52}{1.00}\right) = 57.7°$$.

Next, using the perpendicularity relation gives $$\theta_r = 90° - \theta_B = 90° - 57.7° = 32.3°$$.

We can verify this result by applying Snell's law in the form $$\mu_1 \sin\theta_B = \mu_2 \sin\theta_r$$, which becomes $$1.00 \times \sin 57.7° = 1.52 \times \sin 32.3°$$. Numerically, $$0.845 \approx 1.52 \times 0.534 = 0.812$$, the small difference arising from rounding.

The correct answer is Option (1): 32.3°.