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

Step 1: Understanding the Question:
We are given a scenario where unpolarized light is incident on a glass plate, and the reflected light is completely polarized. This occurs when the angle of incidence is equal to Brewster's angle (\(i_B\)). We need to find the corresponding angle of refraction (\(r\)).
Step 2: Key Formula or Approach:
1. Brewster's Law: The angle of incidence \(i_B\) for which the reflected light is completely polarized is given by \(\tan(i_B) = \frac{n_2}{n_1}\), where \(n_1\) and \(n_2\) are the refractive indices of the first and second media, respectively.
2. Property at Brewster's Angle: When light is incident at Brewster's angle, the reflected ray and the refracted ray are perpendicular to each other. This means \(i_B + r = 90^\circ\).
Step 3: Detailed Explanation:
First, we find Brewster's angle using the given refractive indices:
- \(n_1 = \mu_{air} = 1\)
- \(n_2 = \mu_{glass} = 1.52\)
\[ \tan(i_B) = \frac{1.52}{1} = 1.52 \] The problem provides the value: \(i_B = \tan^{-1}(1.52) = 57.3^\circ\).
Now, we use the property that the reflected and refracted rays are perpendicular. The angle of reflection is equal to the angle of incidence (\(i_B\)). Therefore, the angle between the reflected ray and the surface is \(90^\circ - i_B\), and the angle between the refracted ray and the surface is \(90^\circ - r\). The sum of all angles on a straight line is 180 degrees. The angle between reflected and refracted ray is 90 degrees. So, \(i_B + r = 90^\circ\).
\[ r = 90^\circ - i_B \] Substituting the value of \(i_B\):
\[ r = 90^\circ - 57.3^\circ \] \[ r = 32.7^\circ \] Note: The options in the source PDF may be inconsistent. Based on the data given in the question, the calculated answer is \(32.7^\circ\). We select the answer that logically follows from the provided data.
Step 4: Final Answer:
The angle of the refracted beam with respect to the normal is \(32.7^\circ\).