Question

Sunlight is reflected from a material. The reflected light is 100% polarized at a certain instant. Assuming refractive index of material equal to 1.732, the angle between the sun and the horizon at that instant is

• A. 30°
• B. 45°
• C. 60°
• D. 0°

Hint:

Always be careful about which angle is being asked for in problems involving reflection and refraction. The laws use the angle with the normal, but questions might ask for the angle with the surface (glancing/grazing angle) or the angle of deviation. Drawing a simple diagram of the incident ray, the surface, and the normal can prevent confusion.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
When unpolarized light is reflected from a dielectric surface, the reflected light is completely plane-polarized if the angle of incidence is equal to the polarizing angle, also known as Brewster's angle (\(\theta_p\)). Brewster's Law relates this angle to the refractive index of the material. The question asks for the angle of the sun with the horizon, which is complementary to the angle of incidence.
Step 2: Key Formula or Approach:
1. Brewster's Law: \( n = \tan(\theta_p) \), where \(n\) is the refractive index and \(\theta_p\) is the polarizing angle of incidence. 2. The angle of incidence (\(\theta_p\)) is measured from the normal to the surface. The angle of the sun with the horizon (\(\alpha\)) is the angle measured from the horizontal surface itself. These two angles are complementary: \( \theta_p + \alpha = 90^\circ \).
Step 3: Detailed Explanation:
1. Calculate Brewster's Angle (\(\theta_p\)):
Given the refractive index \( n = 1.732 \).
We recognize that \( 1.732 \approx \sqrt{3} \).
Using Brewster's Law:
\[ \tan(\theta_p) = n = \sqrt{3} \] The angle whose tangent is \(\sqrt{3}\) is \(60^\circ\).
\[ \theta_p = 60^\circ \] 2. Calculate the angle with the horizon (\(\alpha\)):
The angle of incidence (\(\theta_p\)) is the angle between the incoming sunlight and the normal (the vertical line perpendicular to the horizon). The angle between the sun and the horizon (\(\alpha\)) is the angle between the sunlight and the horizontal surface.
From geometry, \( \alpha = 90^\circ - \theta_p \).
\[ \alpha = 90^\circ - 60^\circ = 30^\circ \] Step 4: Final Answer:
The angle between the sun and the horizon is 30°.