Total Internal Reflection

Total internal reflection (TIR) happens when light tries to leave a dense medium (like glass or water) into a less dense medium (like air) at a steep angle and is reflected back inside, as if the surface were a perfect mirror. This is how optical fibres keep light trapped.

Key ideas

• Normal: an imaginary line at 90° to the surface.
• Angle of incidence (i): between the incoming ray and the normal.
• Angle of refraction (r): between the refracted ray and the normal.
• Refractive index (n): how much a material slows light; higher n means light slows more.
• Critical angle (c): the angle of incidence in the denser medium that makes the refracted ray skim along the surface (r = 90°).

When does TIR occur?

• Light must travel from higher n to lower n (e.g. glass to air).
• Increase i: small i → most light refracts out; i = c → refracted ray along the surface; i > c → all light is reflected inside (TIR).
• The reflected ray obeys the mirror rule: angle of reflection = angle of incidence.

Useful equations

Snell’s law (any two media): $n_1 \sin i = n_2 \sin r$.

For a denser medium to air ($n_{air} \approx 1$), the critical angle satisfies:

$$\sin c = \frac{1}{n} \quad \text{so} \quad n = \frac{1}{\sin c}.$$

Simple experiment (semicircular block)

Shine a narrow ray towards the centre of a semicircular glass block so the ray hits the flat face. Rotate the block until the emerging ray just grazes the surface. Measure i at that moment: that angle is the critical angle c.

Real-world applications

• Optical fibres for internet and medical endoscopes: light reflects internally many times with little loss.
• Prisms in periscopes and binoculars: prisms use TIR to reflect light with very little absorption.
• Diamonds sparkle because their high n gives a small c, trapping light inside.

Common misconceptions

• TIR does not occur when light goes from air into glass; it must go from higher n to lower n.
• Angles are measured from the normal, not from the surface.
• At the critical angle the refracted ray does not disappear; it travels along the surface (r = 90°).