Shine a ray of light from glass into air at a steep enough angle and it bounces straight back into the glass — no refraction, total reflection. This phenomenon, total internal reflection, is what makes optical fibres carry internet signals around the world and gives diamonds their dazzling sparkle.
What is refraction and why does it lead to total internal reflection?
Refraction is the change in direction of a light ray when it crosses a boundary between two media with different optical densities (different speeds of light). Light slows down when it enters a denser medium (e.g. glass) and speeds up when it enters a less dense medium (e.g. air).
The key rule: when light travels from a denser medium to a less dense medium (e.g. glass to air), it bends away from the normal (the perpendicular to the boundary). As the angle of incidence increases, the refracted ray bends further and further away from the normal.
At a specific angle — the critical angle — the refracted ray travels exactly along the boundary (at 90° to the normal, along the surface).
Beyond the critical angle, there is no refracted ray at all. Instead, all the light is reflected back into the denser medium. This is total internal reflection (TIR).
What are the two conditions for total internal reflection?
TIR only occurs when both conditions are met:
- Light must travel from a denser to a less dense optical medium (e.g. glass to air, water to air). It cannot occur in the other direction (air to glass).
- The angle of incidence must be greater than the critical angle for that medium–boundary combination.
If only one condition is met, TIR does not occur.
What is the critical angle and how is it calculated?
The critical angle (C) is the angle of incidence (measured from the normal) at which the refracted ray just travels along the boundary (angle of refraction = 90°).
The critical angle depends on the refractive index (n) of the denser medium. For a boundary between the medium and air:
Formula:
sin(C) = 1/n
Where n is the refractive index of the medium.
Worked example: Glass has a refractive index of 1.5. What is the critical angle?
sin(C) = 1/1.5 = 0.667
C = sin⁻¹(0.667) = 41.8° ≈ 42°
So for typical glass: any ray hitting the glass–air boundary at more than 42° from the normal will undergo total internal reflection.
Critical angles for common media (glass–air boundary):
| Medium | Refractive index (n) | Critical angle |
|---|---|---|
| Crown glass | 1.5 | ~42° |
| Dense flint glass | 1.7 | ~36° |
| Diamond | 2.42 | ~24° |
| Water | 1.33 | ~49° |
| Optical fibre (glass core) | ~1.5 | ~42° |
Diamond has an unusually small critical angle (24°) because of its very high refractive index. This means light entering a diamond from almost any direction undergoes multiple total internal reflections before finally exiting from a specific face — contributing to the exceptional brilliance of a well-cut diamond.
How do optical fibres use total internal reflection?
An optical fibre is a thin strand of glass or plastic (the core) surrounded by a layer of a material with a lower refractive index (the cladding). Light entering the core at one end is repeatedly totally internally reflected off the core–cladding boundary, bouncing along the fibre until it exits at the other end.
Key features:
- Because the refractive index of the core is greater than that of the cladding, TIR occurs at every bounce.
- The cladding also protects the core from scratches that would scatter light and disrupt transmission.
- Light travels through the fibre with very low loss — much less than the signal loss in copper wire at the same distance.
Applications of optical fibres:
| Application | How TIR is used |
|---|---|
| Broadband internet | Pulses of infrared laser light carry data at near the speed of light; multiple signals per fibre via different wavelengths |
| Medical endoscopes | Bundles of fibres transmit light to illuminate inside the body; a separate bundle transmits the reflected image back to the doctor |
| Decorative lighting | Light piped from a central source to many fibre ends, each lit without electrical wiring |
Advantages of optical fibres over copper wire cables:
- Much higher data transmission rates (bandwidth)
- Much lower signal loss over long distances
- Immune to electromagnetic interference
- Smaller, lighter, and cheaper per metre for equivalent bandwidth
How is TIR exploited in prisms and periscopes?
Right-angle glass prisms (45°–45°–90°) can replace mirrors using TIR. When a ray hits the hypotenuse face of a right-angle prism at 45° (greater than the critical angle of ~42° for glass–air), it undergoes TIR and is reflected at exactly 90°.
Advantages over a conventional silvered mirror:
- 100% of the light is reflected (silver mirrors absorb some)
- No silver tarnishing over time
- More compact and robust
Applications: periscopes in submarines, binoculars (two prisms fold the light path to give compact body while maintaining image clarity), and cat's eyes on UK roads (prismatic reflectors that return headlight beams back towards the driver).
What happens to the reflected ray during TIR?
The angle of reflection equals the angle of incidence (as with all reflection from a flat surface — the law of reflection). There is no transmitted ray. The energy of the incident ray is completely conserved in the reflected ray — no energy is lost to the second medium. This is why TIR is described as total: total reflection with no energy loss to the other medium.
By contrast, at angles below the critical angle, some light is transmitted (refracted) and some is reflected (partial reflection). Only above the critical angle does all the light reflect.
How should you answer TIR questions in the exam?
For a diagram question showing TIR:
- Draw the normal at the point of incidence (perpendicular to the boundary).
- Mark the angle of incidence (> critical angle).
- Draw the reflected ray: angle of reflection = angle of incidence, on the opposite side of the normal, inside the denser medium.
- No refracted ray should be drawn.
For an explanation question:
- State that light travels from a denser to a less dense medium.
- State that the angle of incidence exceeds the critical angle.
- State that all light is reflected back into the denser medium (no refracted ray).
For optical fibres:
- Explain that the core has a higher refractive index than the cladding.
- Light hits the core–cladding boundary at an angle greater than the critical angle.
- TIR occurs at each bounce; light travels along the fibre with minimal energy loss.
Frequently asked questions
Can total internal reflection occur in water?
Yes. Water has a refractive index of about 1.33 and a critical angle of approximately 49°. If you are underwater and look upwards at an angle greater than 49° from the vertical (the normal to the water surface), the surface appears like a perfect mirror — you see the reflection of the underwater scene. Fish use this phenomenon: a predator looking up through water at an angle below 49° sees above the surface (the "window" through which light enters), while at steeper angles the surface is a mirror. This phenomenon is known as Snell's window.
Why do diamonds sparkle more than glass?
Diamond has the highest refractive index of any natural gem (n = 2.42), giving it a very small critical angle of just 24°. Light entering a well-cut diamond at almost any angle undergoes multiple total internal reflections before exiting. Diamond cutters position the facets precisely so that light enters through the top (table) and exits back through the top after bouncing internally — maximising "brilliance". Glass (n ≈ 1.5, critical angle ≈ 42°) loses more light through the bottom of the stone and produces far less internal reflection and sparkle. Diamond also disperses light into its spectrum colours more strongly, adding the "fire" effect.
What is the difference between partial reflection and total internal reflection?
At any boundary between two media, some light is always reflected (partial reflection), regardless of the angle of incidence. This is why you see your reflection in a window even when most light passes through. When light travels from a denser to a less dense medium, partial reflection occurs at all angles. At exactly the critical angle, the refracted ray travels along the boundary and a large proportion of light is reflected. Above the critical angle, the partial reflection becomes total — 100% of the light is reflected back, with no refracted ray. The sudden transition from partial to total reflection at the critical angle is a sharp boundary, not a gradual change.
Professor Newton at aitutors.me will walk you through TIR ray diagrams, quiz you on the critical angle formula, and help you build up the full optical fibre explanation that examiners want to see.