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. equal to angle of incidence
• B. $90^\circ$
• C. $180^\circ$
• D. $0^\circ$

Answer 1

The Correct Option is B

Total internal reflection is a phenomenon that occurs when a wave, such as light, travels from a medium with a higher refractive index to a medium with a lower refractive index, and the angle of incidence exceeds a specific critical angle. The critical angle is the angle of incidence at which the refracted ray is exactly along the boundary, meaning the angle of refraction is 90 degrees.

To understand why the angle of refraction is 90 degrees when the angle of incidence equals the critical angle, we can refer to Snell's Law, which is given by:

n_1 \sin \theta_i = n_2 \sin \theta_r

Here:

• n_1 and n_2 are the refractive indices of the first and second medium, respectively.
• \theta_i is the angle of incidence.
• \theta_r is the angle of refraction.

When the angle of incidence is equal to the critical angle \theta_c, the refracted ray travels along the boundary with:

\theta_r = 90^\circ

At this critical angle, the sine of the angle of refraction is 1 because:

\sin 90^\circ = 1

Therefore, Snell's Law simplifies to:

n_1 \sin \theta_c = n_2 \sin 90^\circ = n_2 \times 1

This confirms that when total internal reflection occurs and the angle of incidence equals the critical angle, the angle of refraction is 90^\circ.

Conclusion: The correct answer is that the angle of refraction will be $90^\circ$.