Question

When an unpolarized light falls at a particular angle on a glass plate (placed in air). It is observed that reflected beam is completely polarized the angle of refracted beam with respect to the normal is : (Given : \(\tan^{-1}(1.52) = 57.3^\circ, \mu_{air = 1, \mu_{glass} = 1.52\))}

• A. \(57.3^\circ\)
• B. \(32.7^\circ\)
• C. \(28.65^\circ\)
• D. \(61.35^\circ\)

Hint:

A very useful property to remember is that at Brewster's angle, the reflected and refracted rays are mutually perpendicular. This gives the simple relation \(i_B + r = 90^\circ\), which often simplifies calculations.

Answer 1

The Correct Option is B

To solve the problem, we need to understand the concept of light polarization, specifically Brewster's Law. Brewster's angle is the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection.

The refracted and reflected beams are at right angles to each other under this condition. According to Brewster's Law, the angle at which this occurs is given by:

\(\tan(\theta_B) = \mu\)

where \(\theta_B\) is the Brewster's angle and \(\mu\) is the refractive index of the glass with respect to air.

Given:

• Refractive index of glass, \(\mu_{glass} = 1.52\)

Applying Brewster's Law:

\(\tan(\theta_B) = 1.52\)

From the information provided:

\(\theta_B = \tan^{-1}(1.52) = 57.3^\circ\)

For the refracted beam, which is at an angle \(\theta_r\) to the normal:

Using the relationship due to Brewster's angle, \(\theta_B + \theta_r = 90^\circ\) since the reflected and refracted beams are perpendicular to each other at Brewster's angle.

Substituting the value of \(\theta_B\):

\(\theta_r = 90^\circ - 57.3^\circ = 32.7^\circ\)

Thus, the angle of the refracted beam with respect to the normal is 32.7^\circ.

The correct answer is therefore:

• 32.7^\circ