Total Internal Reflection and the Critical Angle

Total internal reflection (TIR) occurs when light travelling inside a denser medium hits the boundary with a less dense medium at an angle greater than the critical angle. All the light is reflected back into the denser medium; none passes through.

Conditions for total internal reflection

Both conditions must be met:

1. Light must be travelling from a denser medium to a less dense medium (e.g. glass to air, water to air).
2. The angle of incidence must be greater than the critical angle.

The critical angle

The critical angle ($c$) is the angle of incidence at which the angle of refraction is exactly 90$^\circ$ (the refracted ray travels along the boundary).

• Below the critical angle: the light refracts (bends away from the normal) and some is reflected.
• At the critical angle: the refracted ray travels along the boundary.
• Above the critical angle: total internal reflection occurs.

Applications

Application	How TIR is used
Optical fibres	Light enters the fibre and hits the inner surface at angles greater than the critical angle. TIR keeps the light inside the fibre, allowing signals to travel long distances
Prisms in binoculars	45$^\circ$-45$^\circ$-90$^\circ$ prisms use TIR to redirect light, providing a longer optical path in a compact body
Cat’s eyes (road reflectors)	Glass beads use TIR to reflect car headlights back to the driver

Worked example

Light travels inside a glass block (critical angle = 42$^\circ$). It hits the glass-air boundary at 50$^\circ$. Describe what happens.

Since 50$^\circ$ > 42$^\circ$ (the critical angle), total internal reflection occurs. All the light is reflected back into the glass. The angle of reflection equals 50$^\circ$.

Common errors and how to correct them

Stating TIR can occur when light goes from air to glass. TIR only happens when light travels from a denser to a less dense medium (e.g. glass to air), not the other way around.

Confusing the critical angle with the angle at which refraction stops completely. At the critical angle, refraction still occurs (at 90$^\circ$). TIR begins when the angle exceeds the critical angle.

How to apply this in an exam

State both conditions for TIR. Draw a clear diagram showing the normal, the incident ray, and the reflected ray. If given the critical angle, compare it with the angle of incidence to determine whether refraction or TIR occurs.