How does light propagate through an optical fibre by total internal reflection?

In one line

An optical fibre guides light because its core has a higher refractive index than its cladding, so light entering within the acceptance angle keeps undergoing total internal reflection and zig-zags along the core.

Explained simply

Think of a ball bouncing along a narrow corridor without ever escaping through the walls. In a fibre, light "bounces" off the core-cladding boundary thousands of times per metre, and because each bounce is a total reflection, almost no light is lost, even around gentle bends.

How it works

Structure:

• Core: central glass or plastic cylinder of index \(n_1\) that carries the light.
• Cladding: surrounding layer of slightly lower index \(n_2\); it makes TIR possible and protects the core surface.
• Buffer/jacket: plastic coating for mechanical strength and protection from moisture.

Propagation:

1. Light from a source enters the core end face from air at angle \(\theta_i\).
2. It refracts into the core at angle \(\theta_r\) and travels to the core-cladding boundary.
3. It meets the boundary at angle \(\theta = 90° - \theta_r\). If \(\theta > \theta_c\), it is totally reflected.
4. Because the geometry repeats, every later reflection is at the same angle, so the ray stays trapped and zig-zags to the far end.
5. Rays entering at too steep an angle hit the boundary below \(\theta_c\), partly refract into the cladding and are lost.

Key formula

Condition for guidance: \(\theta \ge \theta_c\) with \(\sin\theta_c = n_2/n_1\). The largest allowed entry angle is given by \(\sin\theta_a = \sqrt{n_1^2 - n_2^2}\) (from air), where \(\theta_a\) is the acceptance angle.

Quick example

For \(n_1 = 1.50\), \(n_2 = 1.45\), \(\theta_c \approx 75.2°\) and \(\theta_a \approx 22.6°\). So any ray hitting the fibre end within 22.6° of the axis is guided; steeper rays leak into the cladding. This is how light from a laser in Mumbai can travel through undersea cables to another country.

Common mistakes

• Saying the cladding has a higher refractive index than the core.
• Thinking light travels in a perfectly straight line; in multimode step-index fibres it zig-zags.
• Confusing the angle at the end face (acceptance angle) with the angle at the core-cladding boundary (critical angle).

How MU asks it

Asked as "Explain the principle of light propagation in optical fibre" or "Explain the structure of an optical fibre" (3 to 5 marks). Draw the core, cladding and jacket, show a zig-zag ray with angles marked, and write the TIR condition.