Question

In total internal reflection when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be angle of refraction?

• A. 180°
• B. 0°
• C. equal to angle of incidence
• D. 90°

Answer 1

The Correct Option is D

Total internal reflection is a phenomenon that occurs when a light ray traveling in a denser medium hits the boundary with a less dense medium at an angle greater than the critical angle. At this point, all light is reflected back into the denser medium, none passing into the less dense medium.

The critical angle is defined as the angle of incidence at which the angle of refraction is 90°, meaning the refracted ray would travel along the boundary between the two media. This is the angle of refraction at the critical angle, a crucial point in understanding total internal reflection.

To comprehend this better, let us consider the scenario given:

1. Definition of Critical Angle:
   The critical angle (\theta_c) is the angle of incidence in the denser medium at which the angle of refraction in the less dense medium is 90°. This occurs when the refracted ray grazes along the boundary between the two media.
2. Condition for Total Internal Reflection:
   For total internal reflection to occur, the angle of incidence must be greater than the critical angle. At the critical angle, the refracted angle is exactly 90°.
3. Calculating the Angle of Refraction at the Critical Angle:
   By Snell's Law, we have n_1 \sin \theta_c = n_2 \sin 90^\circ, where n_1 and n_2 are the refractive indices of the denser and less dense media, respectively. Since \sin 90^\circ = 1, it confirms that the refracted angle is 90°.

Therefore, when the angle of incidence is equal to the critical angle, the angle of refraction will be exactly 90°, as specified in the question.

The correct answer is 90°.