Total Internal Reflection

This lesson covers total internal reflection (TIR) as required by the Edexcel GCSE Physics specification (1PH0), Topic 5: Light and the Electromagnetic Spectrum. You need to understand the conditions for TIR, the concept of the critical angle, and the practical applications of TIR including optical fibres.

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What Is Total Internal Reflection?

Total internal reflection (TIR) occurs when a ray of light travelling inside a denser medium (e.g. glass or water) hits the boundary with a less dense medium (e.g. air) and is completely reflected back inside the denser medium. No light passes through the boundary — all of it is reflected.

This is different from normal reflection because in normal circumstances some light would pass through (refract) and some would reflect (partial reflection). In TIR, 100% of the light is reflected.

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The Critical Angle

The critical angle is the angle of incidence above which total internal reflection occurs.

What Happens at Different Angles

Angle of Incidence	What Happens
Less than the critical angle	Most light is refracted (passes through the boundary), with some partial reflection
Equal to the critical angle	The refracted ray travels along the boundary (angle of refraction = 90°). This is the boundary case.
Greater than the critical angle	Total internal reflection — all light is reflected back into the denser medium. No refraction occurs.

flowchart LR
    A["Angle of incidence<br/>< critical angle"] --> B["Light mostly refracts<br/>(passes through boundary)<br/>Some partial reflection"]
    C["Angle of incidence<br/>= critical angle"] --> D["Refracted ray travels<br/>along the boundary<br/>(angle of refraction = 90°)"]
    E["Angle of incidence<br/>> critical angle"] --> F["TOTAL INTERNAL<br/>REFLECTION<br/>All light reflected back"]

    style A fill:#3498db,color:#fff
    style C fill:#f39c12,color:#fff
    style E fill:#e74c3c,color:#fff
    style B fill:#3498db,color:#fff
    style D fill:#f39c12,color:#fff
    style F fill:#e74c3c,color:#fff

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Two Conditions for Total Internal Reflection

For TIR to occur, both of the following conditions must be met:

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

Exam Tip: Both conditions must be stated for full marks. A very common mistake is to only state one condition. You must mention both: (1) light going from denser to less dense medium, and (2) angle of incidence greater than the critical angle.

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Calculating the Critical Angle (Higher Tier)

The critical angle (c) is related to the refractive index (n) of the denser medium by the equation:

$\sin c = \frac{1}{n}$sinc=n1​

Where:

• c = critical angle (in degrees)
• n = refractive index of the denser medium (relative to air/vacuum)

Worked Example 1

The refractive index of glass is 1.50. Calculate the critical angle for glass.

$\sin c = \frac{1}{n} = \frac{1}{1.50} = 0.667$sinc=n1​=1.501​=0.667

$c = \sin^{-1}(0.667) = 41.8°$c=sin−1(0.667)=41.8°

The critical angle for glass is 41.8°.

This means any ray of light inside glass that hits the glass-air boundary at an angle greater than 41.8° (from the normal) will be totally internally reflected.

Worked Example 2

The critical angle for diamond is 24.4°. Calculate the refractive index of diamond.

$\sin c = \frac{1}{n}$sinc=n1​

$n = \frac{1}{\sin c} = \frac{1}{\sin 24.4°} = \frac{1}{0.413} = 2.42$n=sinc1​=sin24.4°1​=0.4131​=2.42

The refractive index of diamond is 2.42.

Exam Tip: The higher the refractive index, the smaller the critical angle. Diamond has a very high refractive index (2.42) and therefore a very small critical angle (24.4°), which means TIR occurs easily inside diamonds — this is why they sparkle so much.

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Critical Angles of Common Materials

Material	Refractive Index	Critical Angle
Water	1.33	48.8°
Glass (typical)	1.50	41.8°
Diamond	2.42	24.4°

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Applications of Total Internal Reflection

1. Optical Fibres

Optical fibres are thin, flexible strands of very pure glass that transmit light (or infrared) over long distances using total internal reflection.

How they work:

• Light enters one end of the fibre at a small angle.
• The light hits the inside surface of the fibre at an angle greater than the critical angle.
• Total internal reflection occurs repeatedly, bouncing the light along the fibre.
• The light travels the full length of the fibre without escaping.

Applications of optical fibres:

• Broadband internet — data is transmitted as pulses of light through optical fibre cables. This is faster and has higher bandwidth than copper cables.
• Medical endoscopes — a bundle of optical fibres is inserted into the body to allow doctors to see inside (e.g. examining the stomach or intestines) without invasive surgery.
• Telecommunications — telephone signals are transmitted as light pulses.

Advantages of Optical Fibres Over Copper Cables

Feature	Optical Fibres	Copper Cables
Signal speed	Light speed (very fast)	Electrical signal speed (slower)
Bandwidth	Very high — can carry more data	Lower bandwidth
Signal loss	Very low over long distances	Higher signal loss (resistance)
Interference	Not affected by electromagnetic interference	Can be affected by EM interference
Weight	Lightweight	Heavier
Security	Difficult to tap (intercept)	Easier to tap

2. Cat's Eyes on Roads

Cat's eyes (retroreflectors) are embedded in road surfaces to reflect car headlights back towards the driver. They use two back-to-back prisms. Light enters the prism, undergoes TIR off the back surface, and is reflected back in the direction it came from.

3. Prisms in Binoculars and Periscopes

Right-angled prisms (45°-90°-45°) can be used instead of mirrors to reflect light through 90° or 180° using TIR. The critical angle of glass (~42°) is less than 45°, so TIR occurs at the internal surface.

Advantages of prisms over mirrors:

• Prisms reflect 100% of the light (TIR), whereas mirrors always absorb some light.
• Prisms do not tarnish or degrade over time, whereas mirror coatings can deteriorate.

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Summary