Question

In which of the following, total internal reflection does not occur ?

• A. Twinkling of stars
• B. Brilliance of diamonds
• C. Optical fibre
• D. Reflecting prism

Hint:

To distinguish between refraction and total internal reflection phenomena, look at whether light crosses a boundary or gets trapped inside. Atmospheric effects (twinkling, early sunrise) are caused by continuous bending (refraction), whereas light trapping (fibers, diamonds, mirages) depends on TIR.

Answer 1

The Correct Option is A

Concept: Total Internal Reflection (TIR) is an optical phenomenon that occurs when a light wave travelling through an optically denser medium strikes the boundary of an optically rarer medium at an angle of incidence greater than a specific limiting angle called the critical angle (\(\theta_c\)). The two mandatory conditions for TIR to happen are:
• Light must propagate from a denser medium toward a rarer medium.
• The angle of incidence inside the denser medium must exceed the critical angle: \(i > \theta_c\), where \(\sin\theta_c = \frac{\mu_{\text{rarer}}}{\mu_{\text{denser}}}\).

Step 1: Analyzing each option against the principles of TIR.

• (A) Twinkling of stars: This phenomenon occurs due to continuous atmospheric refraction. Starlight passes through multiple layers of Earth's atmosphere with continuously fluctuating densities and refractive indices. This causes the light path to bend randomly, making the star appear to change position and brightness rapidly. No reflection back into a denser medium happens here.
• (B) Brilliance of diamonds: Diamonds have a very high refractive index (\(\mu \approx 2.42\)), which creates a small critical angle (\(\theta_c \approx 24.4^\circ\)). Diamond cutters exploit this by shaping facets so that light entering the diamond hits internal faces at angles greater than \(24.4^\circ\), causing multiple internal total reflections before escaping, creating its brilliant sparkle.
• (C) Optical fibre: An optical fiber contains a high refractive index core surrounded by a lower index cladding. Light signals fed into the core hit the core-cladding boundary at an angle \(i > \theta_c\), trapping the light inside via continuous total internal reflection along the fiber length.
• (D) Reflecting prism: Right-angled isosceles prisms made of glass (\(\theta_c \approx 42^\circ\)) are structured so that light strikes internal faces at \(45^\circ\). Since \(45^\circ > 42^\circ\), total internal reflection occurs, allowing the prism to turn light beams by \(90^\circ\) or \(180^\circ\) without intensity loss. Since the twinkling of stars is caused by atmospheric refraction rather than total internal reflection, Option (A) is the correct choice.