Question

A light ray falls on a glass surface of refractive index √3, at an angle 60°. The angle between the refracted and reflected rays would be:

• A. 30°
• B. 60°
• C. 90°
• D. 120°

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
When light strikes a transparent boundary, it undergoes both reflection and refraction.
Reflection follows the rule that the angle of reflection equals the angle of incidence.
Refraction follows Snell's Law, relating the angles and the refractive indices of the media.
Key Formula or Approach:
1. Angle of reflection \(i_r = i = 60^\circ\).
2. Snell's Law: \(\mu = \frac{\sin i}{\sin r}\).
Step 2: Detailed Explanation:
1. Find the angle of refraction (\(r\)):
Given \(\mu = \sqrt{3}\) and \(i = 60^\circ\).
\[ \sqrt{3} = \frac{\sin 60^\circ}{\sin r} \]
\[ \sin r = \frac{\sin 60^\circ}{\sqrt{3}} = \frac{\sqrt{3}/2}{\sqrt{3}} = \frac{1}{2} \]
\[ r = \arcsin\left(\frac{1}{2}\right) = 30^\circ \]
2. Determine the angle between the rays:
The incident ray, normal, reflected ray, and refracted ray are all in one plane.
Angle of reflected ray from the normal = \(60^\circ\).
Angle of refracted ray from the normal (on the other side) = \(30^\circ\).
The reflected and refracted rays are on opposite sides of the normal. The total angle between them (\(\phi\)) is given by:
\[ \phi = 180^\circ - (i_r + r) \]
\[ \phi = 180^\circ - (60^\circ + 30^\circ) = 180^\circ - 90^\circ = 90^\circ \]
Step 3: Final Answer:
The angle between the reflected and refracted rays is \(90^\circ\).