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15 Total internal reflection

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Introduction Total internal reflection (TIR) of light may occur when a ray is travelling inside a glass block.The ray reaches the edge of the block; what happens next depends on the angle of incidence i.

Ray passes straight through (i = 0o)

i i

Small i: ray refracted as it leaves the block. Some is reflected

Larger i: ray refracted parallel to edge of block. i = critical angle ci

Even larger i: ray entirely reflected inside the block at the boundary (TIR)

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Total internal reflectionNote there is always a weaker reflected ray as wellTotal – because 100 % of the light is reflectedInternal – because the ray is reflected inside the materialReflection – because the light is reflected, not refracted.

Critical angle CTIR can only happen when the ray travelling through a material of higher refractive index reaches the boundary with a material of lower refractive index.This occurs for any angle of incidence equal to or greater than the critical angle C.

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At the critical angle, i = C and r = 90o.Hence sin i = sin C and sin r = 1 Snell’s law

n =

1sin C

or sin C =

1n

For glass of refractive index 1.5, sin C = 1 / 1.5 = 0.667,

and C = sin-1 0.667 = 42o approximatelyUsing TIR in optic fibresA ray of light can travel inside a solid glass fibre. Each time it reaches the outer surface of the glass, it is reflected back inside, since i is greater than C.

i

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Practical optical fibresOptical fibres are made from glass or plastic, surrounded by a coating of material with a slightly lower refractive index.Rays which travel straight down the centre of the fibre have the shortest route and take least time.Oblique rays have further to travel, and take longer

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coating

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Ray 2 has travelled further than ray 1

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Transmitting dataOptical fibres carry data in digital form. A ray of light from a laser is modulated (switched on and off) at high frequency to encode the data.Rather like Morse code.Problems arise if rays travel along different paths inside the fibre.

A single pulse enters the fibre

The pulse is ‘smeared’: some rays have taken longer than others

This smearing of the pulse is called multipath dispersion.To avoid this problem, most fibres are made with a very narrow core so all rays pass virtually down the middle.

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Advantages of optic fibres

Optic fibres have made possible the Internet. They are used for:Telecommunication networks (carrying telephone messages)Cable televisionLinks between computers (for high speed data transfers).Digital signals are less susceptible to noise than analogue signals.Because of the high frequency of light, optic fibres can carry vastly more data than a current in a cable of comparable size.They are very difficult to bug

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Because the light is only weakly absorbed, signals can travel many kilometres before they become so weak that they need to be re-generated.

Questions 1. Calculate the critical angle for glass of refractive

index 1.62. Calculate the critical angle at the interface

between glass (n = 1.6) and water (n = 1.33)3. Explain why the central core of an optic fibre must

be coated with a material of low refractive index.4. Different wavelengths of light travel at different

speeds through glass. Explain why white light could not be used for long-distance information transfer. Why is laser light more suitable?