Refraction – Learning Outcomes Define refractive index.

Demonstrate refraction.

State the Laws of Refraction.

Solve problems about refraction.

HL: Solve problems about refractive index in terms of

relative speeds.

Give examples of refraction in nature.

Define critical angle and total internal reflection.

Demonstrate total internal reflection.

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Refraction – Learning Outcomes Solve problems about total internal reflection.

Give uses and natural occurrences of refraction.

Discuss transmission of light in optical fibres.

Give uses of optical fibres.

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Refraction Refraction is the bending of light as it passes from one

medium to another.

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To Demonstrate Refraction1. Aim a narrowed beam from a ray box at the side of a

block of glass.

2. Vary the angle of incidence and note that the angle of

refraction increases with angle of incidence.

3. Note that the ray exiting the block is parallel to the

incident ray.

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Laws of Refraction1. The incident ray, the normal at the point of incidence,

and the refracted ray all lie in the same plane.

2. The ratio of the sine of the angle of incidence to the

sine of the angle of refraction is a constant.

The second law is also called “Snell’s Law” which we

must verify experimentally.

The constant in the second law is the refractive index

between the two media, xny, i.e. the ratio of the

absolute refractive indices.

Formula: 𝑥𝑛𝑦 =sin 𝑖

sin 𝑟

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Refractive Index The refractive index of a medium is the ratio of the sine

of the angle of incidence to the sine of the angle of

refraction when light travels from a vacuum into that

medium.

𝑛 =sin 𝑖

sin 𝑟

Material Refractive Index

Vacuum 1 (by definition)

Air 1.0003

Water 1.33

Glass ~1.5 (varies with glass)

Diamond 2.4

Germanium 4.1

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Snell’s Law e.g. A ray of light enters glass from air. The angle of

incidence is 30o and the angle of refraction is 19o. What

is the refractive index of the glass?

e.g. A ray of light enters water from air. If the angle of

incidence is 40o, find the angle of refraction if the

refractive index of water is 1.33.

e.g. Light enters water from glass. If the angle of

incidence is 40o and the angle of refraction is 46.3o,

what is the refractive index between glass and water?

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Depth Due to refraction, objects

immersed in a fluid will

appear to be closer to the

surface than they really are.

This is given by:

Formula: 𝑛 =𝑟𝑒𝑎𝑙 𝑑𝑒𝑝𝑡ℎ

𝑎𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑒𝑝𝑡ℎ

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Depth e.g. Sorcha draws a mark on a sheet of paper and

places a glass block with thickness 8 cm over it. When

viewed from above the glass, the mark appears to be

5.33 cm from the surface. What is the refractive index of

the glass?

e.g. A pool of water is 12 m deep. If the bottom of the

pool is viewed from the air, how deep does it appear?

nwater = 1.33

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Refraction in Nature – Bears Bears have to recognise refraction when fishing – the fish

appears to be higher up than it really is.

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Bear by Joseph Smit – public domain

Real fish by unknown artist – public domain

HL: Speed of Light Light travels at different speeds in different media. The

ratio of speeds between two media is the refractive

index between them.

Formula: 𝑛 =𝑐1

𝑐2

For any medium, it follows that:

Formula: 𝑛 =𝑐 𝑖𝑛 𝑎𝑖𝑟 𝑜𝑟 𝑣𝑎𝑐𝑢𝑢𝑚

𝑐 𝑖𝑛 𝑚𝑒𝑑𝑖𝑢𝑚

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HL: Speed of Light e.g. The refractive index of water is 1.33. If the speed of

light in air is 3 × 108 𝑚 𝑠−1, what is the speed of light in water?

e.g. Light enters glass from air. The angle of incidence is

35o and the angle of refraction is 22o. If the speed of light

in glass is 2 × 108 𝑚 𝑠−1, calculate the speed of light in air.

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Total Internal ReflectionWhen light travels from a denser to a rarer medium, the

critical angle, C is the angle of incidence which gives an

angle of refraction of 90o.

Total internal reflection (TIR) occurs when light travelling

from a denser to a rarer medium is incident at an angle

greater than the critical angle.

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To Demonstrate TIR1. Aim a narrowed beam from a ray box at a semi-circular

slab of glass

2. Aim the beam so that it is incident on the flat face of

the slab internally.

3. Starting with a small angle of incidence, increase this

angle.

4. When the critical angle is reached, the refracted ray

skims along the flat face of the glass.

5. For higher angles of incidence, the refracted ray

changes to a totally internally reflected ray.

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To Demonstrate TIR15

Total Internal Reflection

Given 𝑥𝑛𝑦 =sin 𝑖

sin 𝑟, we can set up the equation for TIR.

If the rarer medium is a vacuum, then:

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𝑛=

sin 𝐶

sin 90𝑜

⇒ 𝑛 =1

sin 𝐶

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Total Internal Reflection e.g. The critical angle for a certain medium is 50o. Find its

refractive index.

e.g. The refractive index of glass is 1.5. What is the critical

angle of glass?

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TIR in Nature – Mirages The refractive index of air changes with temperature.

On hot days, light from the sky can bend away from a

road towards your eye, creating a “puddle” image.

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TIR in Nature – Mirages19

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TIR in Nature – Snell’s Window Looking up while underwater, only light from within a

certain radius will reach you – the rest is totally internally

reflected from underwater. This is called Snell’s window.

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TIR in Nature – Snell’s Window21

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Uses Prism reflectors are used in

road signs to ensure that

light from headlights

reflects back at the driver.

Safety reflectors on bikes

and cars use the same

effect.

Many modern devices use

round reflectors, which

work on the same

principle.

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Uses – Optical FibresOptical fibres are thin transparent glass rods that can

transmit light via total internal reflection.

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Uses – Optical Fibres24

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Optical FibresOptical fibres are used to transmit telephone, television,

and internet signals as pulses of light.

It is better than the old copper cables in pretty much

every way – lower loss, lower size, lower interference.

They are also used in medicine as flexible cameras,

called endoscopes.

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