Question

Explain total internal reflection. Discuss the working of an optical fibre.

Hint:

Light going from a denser to a rarer medium is fully reflected when the angle of incidence exceeds the critical angle, with \( \sin\theta_c = 1/\mu \); a fibre traps light in a high-index core by repeated TIR.

Answer 1

Total Internal Reflection (TIR):
When light travels from an optically denser medium to an optically rarer medium (for example, from glass or water into air), it bends away from the normal. If the angle of incidence in the denser medium is increased, the refracted ray bends more and more towards the surface. At a certain angle of incidence called the critical angle \( \theta_c \), the refracted ray grazes along the boundary (angle of refraction \( = 90^\circ \)). When the angle of incidence is made greater than the critical angle, no light is refracted; the whole of the light is reflected back into the denser medium. This complete reflection of light back into the denser medium is called total internal reflection.

Step 1: Conditions for TIR.
(i) Light must travel from a denser medium to a rarer medium.
(ii) The angle of incidence must be greater than the critical angle, i.e. \( \theta_i > \theta_c \).

Step 2: Critical angle formula.
Applying Snell's law at the critical angle (angle of refraction \( = 90^\circ \)):
\[ \mu \sin\theta_c = 1 \times \sin 90^\circ \]
\[ \sin\theta_c = \frac{1}{\mu} \]
where \( \mu \) is the refractive index of the denser medium with respect to the rarer medium.

Step 3: Working of an optical fibre.
An optical fibre is a very thin, long thread of glass or plastic. It has two parts: a central core of higher refractive index and an outer cladding of lower refractive index. When a light signal enters one end of the core at a small angle, it strikes the core-cladding boundary at an angle greater than the critical angle. Therefore it suffers total internal reflection and is thrown back into the core. This happens again and again along the length of the fibre, so the light travels through the fibre by repeated total internal reflections, even if the fibre is bent, and comes out at the far end with almost no loss of energy.

Step 4: Uses.
Optical fibres are used to carry telephone, internet and television signals over long distances, and in medical instruments (endoscopes) to see inside the human body.

\[\boxed{\text{TIR occurs when } \theta_i > \theta_c,\ \sin\theta_c = \tfrac{1}{\mu};\ \text{optical fibre guides light by repeated TIR}}\]