Total Internal Reflection

This lesson covers total internal reflection (TIR), including the critical angle, the conditions required for TIR, and its practical applications in optical fibres and endoscopes, as required by the Edexcel GCSE Combined Science specification (1SC0).

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What Is Total Internal Reflection?

Total internal reflection (TIR) occurs when a ray of light travelling in a denser medium hits the boundary with a less dense medium at an angle greater than the critical angle. Instead of refracting (passing through), the light is completely reflected back into the denser medium.

The Three Conditions for TIR

For total internal reflection to occur, all three of the following must be true:

1. Light must be travelling from a denser medium towards a less dense medium (e.g. glass → air, water → air).
2. The angle of incidence must be greater than the critical angle for that pair of materials.
3. The boundary must be between two transparent media.

Exam Tip: If the question asks for the conditions for TIR, always state both: (1) light must travel from a denser to a less dense medium AND (2) the angle of incidence must exceed the critical angle. Stating only one condition will lose you a mark.

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The Critical Angle

The critical angle is the angle of incidence at which the refracted ray travels exactly along the boundary (angle of refraction = 90°).

Angle of incidence	What happens
Less than the critical angle	Light refracts (passes through, bending away from normal)
Equal to the critical angle	Light refracts along the surface (angle of refraction = 90°)
Greater than the critical angle	Total internal reflection — light is completely reflected

Critical Angles for Common Materials

Material	Approximate Critical Angle (with air)
Glass (typical)	42°
Water	49°
Diamond	24°

Diamond has a very small critical angle, which means light undergoes TIR many times inside the stone — this is why diamonds sparkle so brilliantly.

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Diagram: What Happens at Different Angles

graph TD
    subgraph "Angle < Critical Angle"
    A1["Incident ray"] --> B1["Refracted ray exits (bends away from normal)"]
    A1 --> C1["Weak reflected ray"]
    end
    subgraph "Angle = Critical Angle"
    A2["Incident ray"] --> B2["Refracted ray along surface (90°)"]
    end
    subgraph "Angle > Critical Angle"
    A3["Incident ray"] --> C3["Totally internally reflected ray"]
    end

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Applications of Total Internal Reflection

1. Optical Fibres

An optical fibre is a thin, flexible strand of glass or plastic that carries light signals over long distances by total internal reflection.

How it works:

• Light enters one end of the fibre and hits the inner surface at an angle greater than the critical angle.
• The light undergoes repeated TIR along the length of the fibre, bouncing from side to side.
• The light travels the full length of the fibre with very little energy loss.

Uses of optical fibres:

Application	Detail
Telecommunications	Carry data (internet, phone calls) as pulses of light — faster and higher capacity than copper wires
Medical endoscopes	Allow doctors to see inside the body without surgery
Lighting	Decorative lights, road signs

Exam Tip: When describing how an optical fibre works, always mention: (1) light enters the fibre, (2) it hits the boundary at an angle greater than the critical angle, (3) total internal reflection occurs repeatedly, (4) light travels along the fibre.

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2. Endoscopes

An endoscope is a medical instrument used to look inside the body (e.g. the stomach, lungs, joints) without invasive surgery.

Structure:

• Contains two bundles of optical fibres:
  • One bundle carries light in to illuminate the internal area.
  • The other bundle carries an image back to the eyepiece or camera.
• The fibres in the imaging bundle are arranged in the same order at both ends (a coherent bundle) so the image is not scrambled.

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3. Prisms and Periscopes

A right-angled prism can be used to reflect light through 90° or 180° using TIR.

• Light enters the prism perpendicular to one face (so it is not refracted on entry).
• It hits the hypotenuse (longest side) at 45°, which is greater than the critical angle for glass (42°).
• Total internal reflection occurs, and the light is redirected.

Applications:

• Periscopes use two right-angled prisms to allow the user to see over obstacles.
• Binoculars use prisms to fold the light path and produce an upright image.
• Prisms are preferred over mirrors because they produce brighter images (less light lost) and do not tarnish over time.

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Worked Example

The critical angle for glass is 42°. A ray of light hits the glass-air boundary at 50°. Describe what happens.

• The angle of incidence (50°) is greater than the critical angle (42°).
• The light is travelling from glass (denser) to air (less dense).
• Both conditions for TIR are met.
• Therefore, total internal reflection occurs — the light is completely reflected back into the glass.
• The angle of reflection equals 50° (law of reflection).

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Worked Example 2

A ray of light hits the glass-air boundary at 30°. The critical angle for glass is 42°. What happens?

• The angle of incidence (30°) is less than the critical angle (42°).
• The light refracts — it passes through the boundary into the air.
• It bends away from the normal (as it enters a less dense medium).

Exam Tip: If you are asked to compare what happens above and below the critical angle, make sure you describe both scenarios clearly for full marks.

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Common Misconceptions

Misconception	Correction
TIR can happen from a less dense to a denser medium	TIR only occurs from a denser to a less dense medium
The critical angle is the same for all materials	Different materials have different critical angles
All of the light is always reflected at a boundary	Below the critical angle, most light is refracted (some is reflected)
Optical fibres use refraction to carry light	They use total internal reflection, not refraction

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Summary

• Total internal reflection occurs when light travels from a denser to a less dense medium at an angle greater than the critical angle.
• At the critical angle, the refracted ray travels along the boundary (angle of refraction = 90°).
• Below the critical angle, light refracts through the boundary.
• Optical fibres use repeated TIR to carry light signals over long distances for telecommunications and medicine (endoscopes).
• Right-angled prisms use TIR to redirect light in periscopes and binoculars.
• Diamond sparkles because its very small critical angle (24°) causes multiple internal reflections.

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What Happens at Each Angle — A Closer Look