Refraction at a plane surface

The arrow and the bent pencil

What you are going to achieve today

What causes waves to refract when they pass across a boundary?What happens to the speed of light waves when they enter a material such as

water?In which direction do light waves bend when they travel out of glass and into

air?Why does a glass prism split sunlight into the colours of a spectrum?

What do we mean by rays?What is Snell’s law?

How is refractive index related to the speed of light waves?

What are the conditions for total internal reflection?How is the critical angle related to refractive index?

Why do diamonds sparkle?

You will be able to answer these questions

Refraction

Refraction is the changing direction of light when it goes into a material of different

density

Set up a pyramid prism to see how different frequencies of light bend bydifferent amounts while going through the prism

The Normal line

The normal line is 90 degrees from the plane surface.

Right angle to the mirror

5b mirror reflection.swf

Normal on a curved surface

Which way does the light travel?

When going in to the block?Towards the normalWhen coming out of the blockAway from the normal?

8 Prism.swf 9 lenses.swf

Snell’s Law

• The refractive index (n) and v explained on next slide

What is the refractive index

• The refractive index (n)of a medium is the speed of light in vacuum (C) divided by the speed of light in the medium (V)

• It is the "optical density" of the medium. It is always greater than 1

n = C/V

Vacuum: n = 1 exactlyAir: n = 1.0003, often approximated by 1

Water: n = 1.34, average over visible rangeGlass: n = 1.5 is typically used in optics homework problems

Fused silica (pure SiO2 glass): n = 1.4

Vacuum: n = 1 exactlyAir: n = 1.0003, often approximated by 1

Water: n = 1.34, average over visible rangeGlass: n = 1.5 is typically used in optics homework problems

Fused silica (pure SiO2 glass): n = 1.4

Common refractive indexes

Quick Refraction

The speed of light in a certain glass is 1.8 10 8 m s-1 . What is the refractive index of the glass?

2. The refractive index of diamond is 2.4. What is the speed of light in diamond?

3. The refractive index changes with the colour of the light leading to dispersion. If the refractive index for blue light in a certain glass is 1.639 and for red light is 1.621, calculate the angle between the rays if they were both incident at 50o

n = C/VC = 3 x 108 in air n (air) = 1

Answersng = c/vg = 3.0 108 / 1.8 108 = 1.67 (no unit as refractive index is a number)

2. nd = c/vd so vd = c/nd = 3 108 m s-1 / 2.4 = 1.25 10 8 m s-1

1 sin θ1 = n2 sin θ2

3. For blue light, sin θ1 = sin 50° / 1.639 = 0.4674 and θ = 27.86o

For red light, sin θ1 = sin 50° / 1.621 = 0.4726 and θ = 27.20o

The angle between the two rays is the difference so = 0.86o. [NB with a prism red is deviated least (“red tries to go straight ahead” pronounce

‘ahead’ as “a red”), useful to learn. The diffraction grating spreads out the colours with blue deviated most.)

n = C/V

n1 =1 n2 =0.4674

The Endoscope

There are two optical fibres

One for light, to illuminate the inside of the patient

One for a camera to send the images back to the doctor. Key hole surgery

Total Internal Reflection

Normal line

This has to be equal or greater than 90 degrees

Sin 90 = 1

Sinθc = n2/n1

Θc is the critical angle

n1 = refractive index of the glass (1.5)

n2 = refractive index of the air (1.001)

Sin-1 (1.001 / 1.5)Critical angle = 41.8

n1Sinθ1 = n2

n = 2.41

Diamonds sparkle

Calculate the critical angle for a diamond

Sinθc = n2/n1

Fibre optics

Refraction Questions1. Explain why substances with a high refractive index like diamond,

sparkle.

2. A pulse of white light is sent straight down a fibre optic cable 1 km long. The refractive index for blue light is 1.639 and for red light 1.621. What time interval will there be between the two components when they reach the far end?

3. Calculate the critical angle of an optical fibre:a) without cladding if the glass has a refractive index of 1.56.b) when cladding is added of n = 1.49c) what advantage is this?

n = C/VSinθc = n2/n1

C = 3 x 108 m/s

nair = 1.01

Speed = Distance/ time

1) As any angle larger than critical is totally internally reflected, the smaller the critical angle the easier it is to get internal reflections which cause the

sparkle.

The speed of the blue light, Vb = c/1.639 = 1.830 × 10 8

m s-1

The speed of the red, Vr = c/1.621 = 1.851 × 10 8 m s-1

time = distance / speed

time taken by the blue light = 1.0 × 103 / 1.830 × 108 = 5.46 μstime taken by the red = 1.0 × 103 / 1.851 × 108 = 5.40 μs

the time lag is 0.06 μs.

3. a) (just glass) sin θc = 1/nglass = 1/1.56 = 0.641 so C =

39.9o

glass and cladding sin θc = 1.49/1.56 and C = 72.8o.

Total Internal Reflection

Normal line

This has to be equal or greater than 90 degrees

Sin 90 = 1

Sinθc = n2/n1

To do at home

Read pages 188- 194

Answer question on page 208

Q1, Q2 (sketch the diagram)