Physics

3.12 - Total Internal Reflection

5 min

note 1 of 5

Total internal reflection depends on the critical angle

Under the right conditions, light meeting a boundary is reflected entirely back into the material it came from. This is total internal reflection.
Total internal reflection can only happen when:
1. Light travels from a denser material (such as glass or water) towards a less dense material (such as air).
2. The angle of incidence is greater than the critical angle.
The critical angle ( $C$ ) is the angle of incidence in the denser material that produces an angle of refraction of 90 degrees in the less dense material. For glass to air, this is about 42 degrees.

What happens at each angle of incidence

Below the critical angle - Most light refracts out into the less dense material, and a small amount is internally reflected.
At the critical angle - The refracted ray travels along the boundary, and there's strong internal reflection.
Above the critical angle - No light escapes; it's all reflected back into the material. This is total internal reflection.

$Three panels labelled below critical angle, at critical angle and above critical angle show a ray meeting a boundary from below and in turn refracting out, travelling along the boundary, then totally internally reflecting.$

note 2 of 5

Formula for the critical angle

$\sin C = \frac{1}{n}$

Where:

$C$ = Critical angle, in degrees
$n$ = Refractive index of the material (no units)

The critical angle of a material-to-air boundary is linked to the refractive index of the material.

The higher the refractive index, the smaller the critical angle. For example, water has a critical angle of about 49 degrees, while glass (which has a higher refractive index) has a critical angle of about 42 degrees.

note 3 of 5

Worked example - Critical angle of glass

A type of glass has a refractive index of 1.52. Calculate the critical angle for a glass-to-air boundary. Give the answer to the nearest degree.

Step 1 - Formula

$\sin C = \frac{1}{n}$

Step 2 - Substitution and calculation

$\sin C = \frac{1}{1.52} = 0.658$

$C = \sin^{- 1} (0.658) = 41.1 \dots^{\circ}$

$C = 41^{\circ} (to the nearest degree)$

note 4 of 5

Optical fibres use total internal reflection

Optical fibres carry light signals using total internal reflection.
A fibre has a dense central core surrounded by cladding of a lower refractive index.

How light stays in the core

Light enters the core at a shallow angle.
Each time it meets the core-cladding boundary, it strikes at an angle greater than the critical angle, so it totally internally reflects and bounces along inside the core.
If a fibre is bent too sharply, light can meet the boundary below the critical angle and escape by refraction into the cladding.

An S-shaped optical fibre, its grey outer layer labelled cladding and the blue tube inside labelled core, carries a light ray that enters at the left and zigzags inside the core to the right.

Use in telecommunications

Used in broadband internet and telephone cables, where data is encoded as pulses of light.
An optical fibre carries far more information than a copper cable of the same diameter and produces higher quality signals.

note 5 of 5

Prisms and periscopes use total internal reflection

Total internal reflection allows prisms to change the direction of light, which is how a periscope works.
Light enters a first prism, strikes the inside surface at an angle greater than the critical angle (45 degrees is greater than 42 degrees for glass), and is totally internally reflected through 90 degrees.
It travels down to a second prism, where it's totally internally reflected through another 90 degrees.
The light emerges travelling in its original direction but at a different height, allowing an observer to see over or around obstacles.

Two triangular glass prisms, one above the other and labelled prisms, turn a ray arriving from the right downwards, then leftwards to a drawn eye, with total internal reflection labelled at each sloping face.

key terms

TermDefinition

Total internal reflectionThe complete reflection of light back into a material when it meets a boundary with a material in which light travels faster (for example from glass into air), at an angle of incidence greater than the critical angle.

Critical angleThe angle of incidence in a denser material that produces an angle of refraction of exactly 90 degrees.

end of notes

Key points to remember

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3.13 - Sound Waves & HearingNext up

Total internal reflection depends on the critical angle

Under the right conditions, light meeting a boundary is reflected entirely back into the material it came from. This is total internal reflection.

Total internal reflection can only happen when:

Light travels from a denser material (such as glass or water) towards a less dense material (such as air).
The angle of incidence is greater than the critical angle.

The critical angle (

C

) is the angle of incidence in the denser material that produces an angle of refraction of 90 degrees in the less dense material. For glass to air, this is about 42 degrees.

What happens at each angle of incidence

Below the critical angle - Most light refracts out into the less dense material, and a small amount is internally reflected.

At the critical angle - The refracted ray travels along the boundary, and there's strong internal reflection.

Above the critical angle - No light escapes; it's all reflected back into the material. This is total internal reflection.

Formula for the critical angle

$\sin C = \frac{1}{n}$

Where:

C

= Critical angle, in degrees

n

= Refractive index of the material (no units)

The critical angle of a material-to-air boundary is linked to the refractive index of the material.

Optical fibres use total internal reflection

Optical fibres carry light signals using total internal reflection.

A fibre has a dense central core surrounded by cladding of a lower refractive index.

How light stays in the core

Light enters the core at a shallow angle.

Each time it meets the core-cladding boundary, it strikes at an angle greater than the critical angle, so it totally internally reflects and bounces along inside the core.

If a fibre is bent too sharply, light can meet the boundary below the critical angle and escape by refraction into the cladding.

Prisms and periscopes use total internal reflection

Total internal reflection allows prisms to change the direction of light, which is how a periscope works.

Light enters a first prism, strikes the inside surface at an angle greater than the critical angle (45 degrees is greater than 42 degrees for glass), and is totally internally reflected through 90 degrees.

It travels down to a second prism, where it's totally internally reflected through another 90 degrees.

The light emerges travelling in its original direction but at a different height, allowing an observer to see over or around obstacles.