Optics

Total internal reflection and optical fibers

When light travels from a higher- to a lower-index medium above a critical incidence angle, no refracted ray emerges and the light is totally reflected; this guides light in optical fibers.

\sin\theta_c=\frac{n_2}{n_1}\quad(n_1>n_2)

Definition: Critical angle and total-reflection condition

Snell’s law is n₁ sinθ₁ = n₂ sinθ₂. For n₁ > n₂, the refracted ray grazes the interface (θ₂ = 90°) at the critical angle, sinθc = n₂/n₁. Total internal reflection occurs only when light travels from higher to lower index and θ₁ > θc.

Vary incidence angle and refractive indices to observe reflected and refracted rays and the critical-angle threshold; light is confined only when the total-reflection condition holds.

Model and quantities

Example: Critical angle at a glass–air boundary

A ray in glass n₁ = 1.50 reaches a glass–air boundary (n₂ = 1.00). Find the critical angle.

Solution

sinθc = 1.00/1.50 = 2/3, so θc = arcsin(2/3) ≈ 41.8°. Incidence in the glass above this angle gives total internal reflection.

Quick check

The critical angle obeys $\sin heta_c=n_2/n_1$ when light travels from higher index $n_1$ to lower index $n_2$ . Total internal reflection occurs only above this angle, with the incident ray in the higher-index medium. In an optical fiber, the core has a higher refractive index than the cladding, so repeated total internal reflections confine light to the core. Fibers carry signals with low loss and provide electrical isolation, making them useful in telecommunications and medical endoscopy.If a fiber is bent too sharply, some light can escape; fiber geometry and materials are chosen to limit this loss.

Light traveling from glass into air at an incidence angle greater than the critical angle will:

When can total internal reflection occur?

References

David Halliday, Robert Resnick, Jearl Walker (2018). Fundamentals of Physics