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 propagating wave strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. The critical angle is the angle of incidence above which the total internal reflection occurs.

To understand this concept, we need to know the condition of the critical angle. The critical angle (\theta_c) can be defined as the angle of incidence which provides an angle of refraction of 90°.

Explanation:

• The critical angle is the angle of incidence for which the angle of refraction is 90°, meaning the refracted ray travels along the boundary.
• For angles of incidence greater than the critical angle, the wave does not pass through the boundary at all, and total internal reflection occurs.
• Mathematically, the critical angle for a medium with refractive index n_1 being denser than the other medium with refractive index n_2 is given by the formula: \theta_c = \sin^{-1}\left(\frac{n_2}{n_1}\right).

Let's now address the question:

• Given that the angle of incidence is equal to the critical angle, the angle of refraction according to the refraction law (Snell's Law) would be 90°.
• Snell's Law states: n_1 \sin(\theta_1) = n_2 \sin(\theta_2), where \theta_1 is the angle of incidence and \theta_2 is the angle of refraction.

Conclusion:

When the angle of incidence is equal to the critical angle, the angle of refraction is 90°, which leads to the refracted ray running parallel to the boundary of the medium. Hence, the correct answer is 90°.