AN INTRODUCTION TO
LIGHT
FOR PHYSICS STUDENTS
COLOUR PHOTONS DISPERSION SPECTRUM WAVES DIFFRACTION
INTERFERENCE POLARISATION ELECTROMAGNETIC GRATING INFRARED
COLOUR PHOTONS DISPERSION SPECTRUM WAVES DIFFRACTION
INTERFERENCE POLARISATION ELECTROMAGNETIC GRATING INFRARED
COLOUR PHOTONS DISPERSION SPECTRUM WAVES DIFFRACTION
INTERFERENCE POLARISATION ELECTROMAGNETIC GRATING INFRARED
COLOUR PHOTONS DISPERSION SPECTRUM WAVES DIFFRACTION
INTERFERENCE POLARISATION ELECTROMAGNETIC GRATING INFRARED
COLOUR PHOTONS DISPERSION SPECTRUM WAVES DIFFRACTION
INTERFERENCE POLARISATION ELECTROMAGNETIC GRATING INFRARED
COLOUR PHOTONS DISPERSION SPECTRUM WAVES DIFFRACTION
INTERFERENCE POLARISATION ELECTROMAGNETIC GRATING INFRARED
COLOUR PHOTONS DISPERSION SPECTRUM WAVES DIFFRACTION
in association with the
School of Education, Trinity College Dublin
INTERFERENCE POLARISATION ELECTROMAGNETIC GRATING INFRARED
COLOUR
THIS TOPIC WILL INTRODUCE YOU TO SOME OF HOW HUMANS ‘SEE’ COLOURS
AND WHAT HAPPENS WHEN DIFFERENT COLOURS ARE MIXED.
KEY POINTS
1. Light consists of tiny bundles of energy called photons.
2. The energy that a photon has determines the colour of light that we ‘see’.
3. The colours of the spectrum Red, Orange, Yellow, Green, Blue, Indigo, and Violet correspond to photons of
increasing amounts of energy. (Red the least, violet the most.)
4. White surfaces reflect light of all colours of the spectrum.
5. A surface that looks coloured to us only reflects light in part of the
spectrum. e.g. a blue blouse reflects light in the blue part of the spectrum.
6. The primary colours are red, green and blue (RGB). All colours of the
spectrum can be made by mixing RGB in different proportions.
7. The secondary colours are cyan, magenta and yellow
OTHER POINTS
1. Photons of light are not coloured. The colours you see are created by the retinas at the back of your
eyes sending electrical signals to your brain when photons hit the retina.
2. However, we talk about ‘the colour of light’ as a useful shorthand.
3. Light from the Sun contains all the colours of the spectrum. We call this light ‘white light’.
4. The primary colours RGB can be mixed to form the secondary colours cyan, magenta and yellow as
well as white light.
5. If, for example, equal amounts of R and G lights mix we see the colour yellow. This is a result of the
way our eyes (and brain) work. The R and G photons do not turn into photons of yellow light.
6. Television, and computer, screens give out light in the three primary colours. The amounts of RGB
light, and hence the colours we see, vary depending on the signal sent to the screen.
KEY PRACTICALS
You should see a demonstration of the results of mixing different coloured lights.
USEFUL WEBSITES
There is a large number of web sites that can help you understand the nature of light and what happens when
lights of different colours are mixed. Here is a short selection:
A demonstration of mixing of coloured lights:
http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=56
An explanation of how television screens work:
en.wikipedia.org/wiki/Televisions#Elements_of_a_television_system
en.wikipedia.org/wiki/Cathode_ray_tube
[2]
WARNING
If you look on the internet for information about mixing colours you may get very confused because some sites do not
list red, green, and blue as primary colours. This is because artists mix different coloured paints or dyes rather than
coloured lights. Artists (and printers) use a different system when they describe the paints they use as ‘primary colours’.
You do not have to know anything about this alternative system for your physics course. Just make sure that you check
that the web sites you may visit are clearly talking about mixing lights rather than paints or dyes.
PUZZLES/QUESTIONS
1. You may remember that an object looks white because it reflects all the colours of the spectrum and, for
example, a blue sweater looks blue because it mainly reflects blue light. What do you think happens to light of
all the other parts of the spectrum when it hits the sweater?
2. What do you think is the explanation of why black ink looks black?
3. Lighting the stage in a theatre or at a rock concert is a skilful job. Why does the person responsible for
deciding on the lighting have to be careful about the choices of coloured lights she uses? For example, a rock
band decides to wear a mixture of vivid blue and red clothes. What would they look like if the lighting director
used spotlights giving out green light to light the stage?
4. Some fluorescent lights give out a ‘softer’ light than others. These lights tend to give a very slight pinkish
tinge to the light. Why should you be careful about judging the colour of the clothes that you buy in a shop that
uses ‘soft’ fluorescent lighting? Briefly explain your answer.
5. Suppose you only had a set of red, green and blue lights. How would you mix the lights to make (i) cyan, (ii)
magenta, (iii) yellow light?
6. Why do you think it is better to wear white clothes in summer if you want to keep cool?
7. If you have decided on your answer to question 6, what might be the reason that some women in very hot
countries, e.g. Greece, wear black clothes?
8. Find out why the Sun gives out white light; i.e. all the colours of the spectrum.
FINAL CHECK
At the end of this topic you should be able to:
Name the colours of the spectrum
Name the primary and secondary colours
Explain why, for example, a red object looks red when viewed in white light
Predict the colour of an object when viewed in different coloured lights
[3]
DISPERSION OF LIGHT
THIS TOPIC WILL INTRODUCE YOU TO A PROPERTY OF LIGHT KNOWN AS DISPERSION. DISPERSION OCCURS WHEN
LIGHTS IS SPLIT INTO ITS COMPONENT COLOURS. YOU ALREADY KNOW AN EXAMPLE OF DISPERSION: RAINBOWS.
IN THIS LESSON YOU WILL DISCOVER SOME OTHER EXAMPLES.
KEY POINTS
1. Dispersion occurs when white light is split into its component colours.
2. Dispersion can be shown by passing white light through a prism.
3. Photons with greatest energy (violet light) are affected the most by passing through the prism. Photons with the
least energy (red light) are affected the least.
4. The order of the colours when light passes through a prism is the same as in a rainbow (ROYGBIV).
5. Dispersion also occurs when white light passes through water droplets (e.g. in a rainbow) or gems stones (e.g.
diamonds). It also occurs when white light reflects off the surface of surfaces etched with very fine lines; e.g. a CD.
6. The effects of dispersion of white light by a prism can be reversed by passing the coloured lights back
through a second prism.
7. You should be able to recall from memory the typical diagram for dispersion through a prism:
of wh
Beam
ite lig
ht
RED
ORANGE
YELLOW
GREEN
BLUE
INDIGO
VIOLET
Prism
OTHER POINTS
1. Dispersion can occur whenever white light travels from one substance to another.
2. Dispersion can have some benefits; e.g. it makes jewellery attractive.
3. Dispersion can cause problems; e.g. when using binoculars or a telescope the image can have coloured
edges. (Looking for the coloured edges is a good way of checking the quality of an optical instrument.)
BACKGROUND INFORMATION
Sir Isaac Newton (1642-1727) is credited with being the first person to make a systematic study of dispersion
and published his findings in his book Opticks in 1704. Newton was very interested in light. Indeed, he
invented one of the main theories about the nature of light—you may learn about this in another lesson. As part
of his experiments he passed a beam of sunlight through a prism and projected the spectrum onto a screen. He
also managed to use a second prism to recombine the coloured lights into a beam of white light. At the time
Newton was working there was a great deal of disagreement about the nature of light. Many people disagreed with
Newton’s explanation that his experiments showed that white light was composed of many different colours. For
example, it was thought that the colours were made by some sort of ‘reaction’ between the glass prism and the light.
You will discover in later lessons that some of Newton’s theories about light were (as far as we know now) wrong or at
least not entirely correct.
[4]
KEY PRACTICALS
You should see a demonstration of dispersion caused by white light passing through a prism.
You should also see some other examples of dispersion; e.g. light passing through a gem stone.
USEFUL WEBSITES
Demonstrations/explanations of dispersion
An applet which shows the splitting of white light using a prism:
http://www.physics.uoguelph.ca/applets/Intro_physics/kisalev/java/dispprizm/index.html
A very good applet that shows you dispersion and recombination of white light using prisms:
http://micro.magnet.fsu.edu/primer/java/scienceopticsu/newton/index.html
The following site has a nice explanation of a rainbow, with pictures and an explanation.
(There is some maths as well, but you can ignore it.)
http://mysite.verizon.net/vzeoacw1/rainbow.html
PUZZLES/QUESTIONS
1. When the beam of white light goes through the prism, how many changes of direction does the light make? Where
do these changes of direction take place? How would you describe the changes in direction? (Look carefully at the
diagram of dispersion that you have been give or have drawn during the lesson.)
2. A student decided she would try passing a beam of red light from a laser through a glass prism. What do you
think she would have seen? (Your teacher may allow you to see this experiment to test out your prediction.) Draw a
diagram showing the ray of light, the prism and what happens to the beam.
3. Look at the incomplete diagrams of a dispersion experiment shown below.
B ea
mo
f wh
ite l
ight
Complete the diagram by sketching the
appearance of the spectrum that you
would expect to see.
4. Find out about the care astronomers have to take in dealing with dispersion when they design telescopes, or why
companies that make binoculars also have to take account of dispersion
FINAL CHECK
At the end of this topic you should be able to:
Explain the meaning of dispersion.
Give at least two examples of dispersion
Draw from memory the prism experiment that demonstrates dispersion
[5]
ELECTROMAGNETIC SPECTRUM
THIS TOPIC WILL TELL YOU ABOUT THE ELECTROMAGNETIC SPECTRUM,
AND THE PROPERTIES/USES OF ELECTROMAGNETIC RADIATION.
KEY POINTS
1. The speed of light is approximately.
All electromagnetic waves travel at this speed in a vacuum.
2. Visible light makes up just one part of the electromagnetic spectrum. Other types of electromagnetic radiation are
shown in the diagram below. N.B. the diagram is not to scale, and the figures are meant to give you a guide (don’t think
they are exact!). You should learn the order of the main parts of the electromagnetic spectrum in the order of the energy
values. Also make sure you know that as energy increases frequency increase, but wavelength decreases. (You do not
have to remember all the figures given in the diagram.)
Electromagnetic spectrum
radio waves
10
– 30
to 10
– 24
microwaves
10
– 23
to 10
– 21
infrared
10
– 20
to 10
visible light
– 19
10
– 19
to 10
ultra-violet
– 18
10
– 18
to 10
X-rays
– 17
10
– 17
to 10
gamma rays
– 13
10
– 12
to 10
– 10
Energy/J
Frequency/Hz
3
10 to 10
9
10
10
to 10
12
10
13
to 10
14
10
14
to 10
15
10
15
to 10
16
10
16
to 10
20
10
21
to 10
23
Wavelength/m
5
10 to 1
1 to 10
–3
10
–4
to 10
–6
10
–6
10
–6
to 10
–8
10
–8
to 10
– 12
10
– 12
to 10
– 14
Visible spectrum
red
orange
yellow
700
580
560
green
blue
500
420
Typical wavelengths in nm.
indigo
violet
400
380
–9
Note: 1nm = 10 m
3. Notice that the higher the frequency and shorter the wavelength, the higher is the energy.
4. The colours of the visible spectrum Red, Orange, Yellow, Green, Blue, Indigo, and Violet correspond to
photons of increasing amounts of energy. (Red the least, violet the most.)
OTHER POINTS
Here is some background information about light that you may find helpful to know about, especially later
in your course.
1. Photons of visible light, and all other parts of the electromagnetic spectrum have an electric field and a
magnetic field associated with them.
2. Photons carry energy and can show properties of both waves and particles.
The energy of a photon is given by
, or
where h is Planck’s constant, c is the speed of light, f is the frequency and the λ wavelength.
[6]
3. Light waves are transverse waves (the wave motion is at right angles to the direction of travel). This diagram is here to
help you visualise a light wave. You do not have to know the details for your Leaving Certificate examination.
Y
Electric field shown in red
X
Magnetic field shown in blue
Direction of travel
This diagram gives you a better
idea of how the electric field
(shown by the red lines)
changes as the photon travels
(from left to right).
PUZZLES/QUESTIONS
1. Look on your radio and find out the wavelength of the RTE Radio 1 and those of one or two other radio stations.
2. Do some research to find out some information about gamma rays. For example, when were they discovered?
Where do gamma rays come from? Can gamma rays pass through you and other objects on Earth? (By the way,
gamma rays are often given the Greek letter gamma, γ as a symbol.)
3. Why are X-rays important for us? Find out when X-rays were discovered, and who discovered them.
4. Physicists have generally agreed that the universe started with a ‘big bang’. Find out how the ‘big bang’ and
microwaves are linked.
5. A student wrote the following account about microwave ovens: ‘Microwave ovens work because the microwaves
they produce cause molecules in food to rotate and vibrate more quickly. That is, the molecules in the food take in
energy provided by the microwaves.’ Find out if the student was correct.
6. It can be fashionable to have a tanned skin. Some people go to ‘tanning shops’ where they lie under a set of
ultraviolet lamps in order to get tanned. What is happening to skin when it tans? Why can it be very dangerous to get
sunburnt, and why is not a good idea to try to keep skin permanently tanned by using ultraviolet lamps?
FINAL CHECK
At the end of this topic you should be able to:
Name the main regions of the electromagnetic spectrum
State the order of energies of the main regions of the electromagnetic spectrum
Know that higher energy goes with higher frequency and lower wavelength
Give examples of uses of different types of electromagnetic radiation
[7]
[8]
INTERFERENCE OF LIGHT
THIS TOPIC WILL INTRODUCE YOU TO THE PROPERTY OF LIGHT WAVES CALLED ‘INTERFERENCE’.
YOU MAY HAVE MET THE IDEA ALREADY WHEN YOU LEARNT ABOUT WAVES IN GENERAL.
INTERFERENCE OF LIGHT IS RESPONSIBLE FOR SOME BEAUTIFUL EFFECTS, LIKE THOSE SHOWN IN THE PICTURES. AFTER
STUDYING THIS TOPIC YOU SHOULD BE ABLE TO EXPLAIN HOW INTERFERENCE OF LIGHT WAVES CAN CAUSE THESE EFFECTS.
KEY POINTS
1. There are two main properties of waves:
(i) waves can show interference
(ii) waves can be diffracted.
2. Two waves interfere when they overlap.
INTERFERENCE
Peaks of both waves overlap perfectly, and
troughs of both waves overlap perfectly
Peaks of one wave overlap perfectly
with troughs of another wave
Peaks and troughs of one wave don’t match
with peaks and troughs of the other wave
Constructive
Destructive
Complete
No
No
Complete
Partial
Partial
Figure 1
Example of
complete
constructive
interference
The ‘red’ and ‘blue’ waves have their crests and troughs in exact sequence; i.e. where there
is a peak in one there is a peak in the other. Also the positions of the troughs match.
These waves will show complete constructive interference, shown by the ‘green’ wave.
Figure 2
Example of
complete
destructive
interference
The ‘red’ wave is half a wavelength ahead of the ‘blue’ wave. The waves
will show complete destructive interference (green line = no wave) because
the peaks of one overlaps the troughs of the other (and vice-versa).
[9]
3. When waves with different wavelengths or frequencies overlap, the interference patterns can vary greatly in their
appearance.
Figure 3 A wave (shown in green) that has a very odd appearance
because it is the result of neither perfect constructive nor perfect
destructive interference of the red and blue waves
OTHER POINTS
1. You need to know the meaning of the terms wavelength (λ), frequency (f) and amplitude (A) to describe
waves.
2. When two waves have their peaks and troughs coinciding, we say they are ‘in phase’. When the peaks
and troughs don’t coincide, they are ‘out of phase’.
3. Interference is responsible for the colours you can see on soap bubbles, the colours of the feathers
of many birds, and the coloured patterns made if oil or petrol spills on water. To understand how these
things happen, see below.
KEY PRACTICALS
You should see illustrations of interference using light waves.
USEFUL WEBSITES
These sites have some nice graphics and explanations of interference:
micro.magnet.fsu.edu/optics/lightandcolor/interference.html
sol.sci.uop.edu/~jfalward/lightinterference/lightinterference.html
This site has an explanation of why peacock feathers have such marvellous colours. It is a little technical, but
basically it is about interference—and it has some nice pictures:
hyperphysics.phy-astr.gsu.edu/hbase/vision/peacock.html
This site gives instructions on how to see interference patterns for yourself:
www.exploratorium.edu/snacks/bridge_light.html
[10]
EXPLANATION OF INTERFERENCE
Two waves will only be synchronised if their peaks and troughs exactly coincide. Otherwise they will suffer destructive
interference. For example, only the waves the top two waves in the diagram below will give constructive interference. But
suppose the ‘blue’ wave stays a little behind the ‘red’ wave so it lags behind a little. In this case the peaks (and troughs)
of the two waves do not coincide. These waves will show destructive interference. However, if the ‘blue’ wave lags behind
by exactly one wavelength, then all will be well, and the two waves interference constructively again. With a little thought
you should realise that the two waves will also interfere constructively if the distances they travel differ by two whole
wavelengths, or by three, four, five etc. whole wavelengths.
In general constructive interference will occur if the paths travelled differ by a whole number (n) of wavelengths (λ).
In symbols this we can show this difference as nλ
A
B
A
C
D
C
B
Figure 4
How constructive
and destructive
interference
depends on the
way waves
overlap.
D
Less than one wavelength causes partial destructive interference
B
A
C
D
A difference of exactly half of a wavelength causes complete destructive interference
A
B
C
D
One complete wavelength causes complete constructive interference
[11]
SOME EFFECTS OF INTERFERENCE
First, a warning: what follows is a simplified explanation of interference effects when light reflects off surfaces. You will
not be led too far astray by the explanation, but (as always) life is more complicated than one might think when you get
down to the details. However, here goes:
Imagine there two surfaces of a thin film of oil with a beam of laser light shining
on them as shown in the diagram. The beam can reflect off the top surface and the
bottom surface. The two beams are shown as T and B. You can see that beam B
has had to travel further than beam T. The extra distance is (very roughly) twice
the gap between the surfaces. Now we know that if the two waves are exactly a
wavelength different then they will constructively interfere; but if not there will
be destructive interference. If you have understood that, you should also be able
to understand why a beams of green light, or yellow light etc. would also be
affected by being reflected off the two surfaces. However, because the different
coloured lights have different wavelengths, the amount of interference they
suffer will also be different.
B
The extra distance travelled by the
bottom ray is shown in blue
Now think what happens if a beam of white light (that contains all the colours of the rainbow) reflects of the two
surfaces. Depending on the angle they make with the surfaces, and the width of the gap, we might see one colour
almost completely removed by destructive interference, and another colour almost unaffected if it suffers
constructive interference.
Finally, think of taking a close-up view of a film of soap. Although it is very thin, it has a front and a back, and light
can reflect off both surfaces. That is why a soap bubble can show so many strange coloured effects when light shines
on it.
PUZZLES/QUESTIONS
1. To understand why many birds have highly coloured feathers you need to know a little biology and a little physics.
Biologists will talk about the colours as part of the display that birds use when choosing a mate, or their use in
camouflage. Physicists will notice that birds, especially duck, have an oily layer on their feathers to keep the water
off. Now you know about the oily layer, explain what interference of light might have to do with the colours we see
on a duck’s wings.
2. Next, do some thinking about why petrol spilled onto water has a strangely coloured appearance. Write a brief
explanation. Or, better, work with others in your group to make a poster that explains this effect, and other examples
of interference of light. The poster should be designed so that it can be put up in your school to explain interference
to other students.
3. The web site physics.bu.edu/py106/notes/Thinfilm.html gives the full story about interference of light reflecting
from thin films such as oil on water or a soap bubble. You might like to check out which important feature of reflection
of light from surfaces were missed out in the simplified explanation above. Hints: what happens to a light wave when
it bounces off the top surface?
4. You will also study diffraction of light. Do some research to find out what diffraction is about, and why you need to
know about interference to explain diffraction.
FINAL CHECK
At the end of this topic you should be able to:
Explain how light waves can produce constructive and destructive interference
Give two examples of interference effects with light
[12]
DIFFRACTION
THIS TOPIC WILL INTRODUCE YOU TO
THE DIFFRACTION OF LIGHT WAVES.
KEY POINTS
1. Diffraction is the spreading out of a wave front
when a wave meets an obstacle or an obstacle
with an opening in it. For example, a water wave
that enters the opening of a harbour will be
diffracted, as shown in the picture of Humboldt
Harbor, Oregon, USA (see http://online.
redwoods.cc.ca.us/instruct/colloquium/).
2. A beam of light can be thought of as a ‘plane wave’ made up of lots of small spherical waves moving together:
Plane waves can be thought
of as a set of spherical wave
fronts moving together.
This idea was first used in 1680 by Huygens, an early Dutch scientist.
Diffraction at an edge
explains why you can
hear sounds round corners.
This wavefront can spread
out through the opening
3. One way of describing diffraction is to say
that when a wave meets the opening, the opening
acts like a source of spherical waves.
and the person.
4. Sound waves are easily diffracted.
That is why you can hear someone speak
even if there is an obstacle between you
5. Using a diffraction grating with laser light is the best way of showing diffraction of light
[13]
OTHER POINTS
1. In spite of what you might have been told in Junior Certificate Science, light can also ‘turn round corners’ because
light is also diffracted when it meets an obstacle. However, because the wavelength of light is so much shorter than
sound waves, the amount of diffraction is much smaller. In fact it is so small that we can’t see it unless we do a
suitable experiment to show the effect.
2. As a rule, diffraction only shows up clearly when the size of the obstacle/opening is about the same dimensions
as the waves involved. For example, sea waves may have wavelengths of many metres, so a wide gap like a
harbour entrance can show diffraction with sea waves; sound waves range from (about) 20m to fractions of a
centimetre, so diffraction of sound waves can happen with obstacles that we are used to, e.g. walls or
doorways. Light waves have wavelengths of the order of 10-7m so only very small openings give diffraction with
light.
KEY PRACTICALS
You should see experiments that illustrate diffraction and perform an experiment to measure the
wavelength of light from a sodium lamp.
USEFUL WEBSITES
The following website gives instructions for a very simple way of seeing a diffraction pattern using a lamp
or candle and a couple of pencils:
www.exploratorium.edu/snacks/diffraction.html
This site has a simple but effective applet showing diffraction at a single slit:
www.phys.hawaii.edu/~teb/optics/java/slitdiffr/
The BBC site listed has a very simple animation of diffraction at a single slit:
http//www.bbc.co.uk/schools/gcsebitesize/physics/waves/water_wavesrev5.shtml
DIFFRACTION OF LIGHT
The colours of the
rainbow are made
visible by sunlight
diffracting from the
surface of an
ordinary CD.
[14]
Our task is to explain how diffraction can happen with light. The main example you need to know is called Young’s double
slit experiment. The experiment consists of a beam of light of one colour (i.e. monochromatic light) shining on a screen
that has two very narrow slits cut in it. Usually a laser is used as the source of light. After passing through the slits, the
light makes a series of regularly spaced spots on a screen some distance from the slits.
A diffraction pattern obtained by
passing red laser light through a
double slit
In Figure 1 below, you can see a very much enlarged diagram that represents two light waves coming from the two
slits in a screen.
These two waves
will show constructive
interference
Laser light
Diffraction grating
elled
ce trav
Distan
D
e trav
istanc
elled b
y ‘blue
’ wave
by ‘red
’ w ave
trav
er than
is long
elled b
y the ‘r
ve
ed’ wa
The waves will have peaks and troughs that overlap only if a whole number of wavelengths will
fit in the ‘gap’
Figure 1 Diagram representing two waves coming from two slits in a screen
The two waves will only be synchronised if their peaks and troughs exactly coincide. Otherwise they will suffer destructive
interference. For example, only the top two waves in Figure 2 below will give constructive interference. But suppose the
‘blue’ wave has had to travel further than the ‘red’ wave so it lags behind a little. In this case the peaks (and troughs) of
the two waves do not coincide. These waves will show destructive interference. However, if the ‘blue’ wave lags behind by
exactly one wavelength, then all will be well, and the two waves interference constructively again. With a little thought you
should realise that the two waves will also interfere constructively if the distances they travel differ by two whole
wavelengths, or by three, four, five etc. whole wavelengths.
[15]
In general constructive interference will occur if the paths travelled differ by a whole number (n) of wavelengths (λ). In
symbols this we can show this difference as nλ On the other hand, if one wave is exactly half of a wavelength in front
(or behind) the other, there will be complete destructive interference.
A
B
A
C
D
C
B
Figure 2
If two waves
differ by an
exact number
of wavelengths,
they will
constructively
interfere
D
Less than one wavelength causes partial destructive interference
B
A
C
D
One complete wavelength causes complete constructive interference
If we return to Figure 1 and show the slits in more detail, we can work out an important formula that
describes the result of a diffraction experiment. See Figure 3.
P
Call this angle theta, θ
Figure 3
Deriving the
two slit
diffraction
formula
θ
Call this
d
distance
R
Q
θ
This angle is theta also
In the triangle PQR, the extra distance the ‘blue’ wave has to travel is the length QR. Therefore, for constructive
interference, QR = nλ.
[16]
But the formula for the sine of an angle is
so in this triangle we have
If we multiply both sides by d, we have the key formula
The value of n gives the order of the spectrum. If you see a diffraction experiment in class you will find that the diffraction
pattern looks rather like that shown below.
Notice that the pattern is symmetrical—there are as many lines above as below the mid-point of the screen. That is,
there always two first order lines (n = 1), two second order lines (n = 2) and so on.
USING THE DIFFRACTION FORMULA
EXAMPLE 1
Here is a typical question that you might be asked.
Suppose a double slit diffraction grating was set up 1m from a screen. The slits were 10-5m apart. Yellow light from
a sodium lamp was shone on the slits. Sodium light has a wavelength of 5.89 x 10-7m. Where would you expect to
find the first order lines? That is, in Figure 4 what is the distance BC?
Angle
θ
Figure 4
Diagram for
diffraction
pattern
calculations
D
C
d
B
A
Second order
lines
Zeroth order
line
1m
Using our formula
First order
lines
we have: n = 1, λ = 5.89 x 10-7m, d = 10-5m
So,
To find the size of the angle, you can either look in a table of sines, or use a calculator or computer. Either way, you
should find that θ = 3.38˚.
Now look at the triangle ABC in Figure 4. You should see that
Therefore
[17]
EXAMPLE 2
Now let us see how we can use the formula to discover the wavelength of the light used in a diffraction experiment using
a diffraction grating.
Suppose red light from a laser produced a diffraction pattern with the second order spots an average of 6.2cm from
the centre of the pattern. In Figure 4 this means that BD = 6.2cm
Also, assume that the screen was 1m from the grating and that the grating used had a spacing of d = 2 x 10-5m
First we change all the distances to be measured in metres.; i.e. BD = 0.062m
Then we use
order spots).
with n = 2 (because we are told we are using information about second
This gives
So, to find the wavelength, we need to calculate the angle, θ. We do this by looking at the diagram of
Figure 4. We know that AB = 1m and BD = 0.062m. So,
Using tables or a calculator, we find
Finally going back to our edition for the wavelength,
The wavelength of this light corresponds to the red part of the spectrum.
QUESTIONS/PUZZLES
1. Thomas Young is credited with discovering diffraction when light passes through double slits. When
was Young alive? Why was Young’s double slit experiment important for theories of light? What else did
Young discover?
2. In a double slit diffraction experiment, the first order lines were at an angle of 2.2°. The slits were
1.5 x 10-5m apart. (i) What was the wavelength of the light? (ii) At what angle would the second order lines
appear?
3. If you had done the experiment mentioned in question 2, what distance from the central (zeroth order)
line would the first order lines have been found? Assume the slits were 2.5m from the screen.
4. A diffraction grating was marked as having lines spaced 1.25 x 10-6m apart. When this grating was
used with a source of light of one colour, the angle between the two first order lines was found to be 56.3°.
(i) What is the size of the angle in the formula nλ = dsinθ? (ii) What was the wavelength of the light?
FINAL CHECK
At the end of this topic you should be able to:
Explain how light waves can produce a diffraction pattern in a double slit diffraction experiment
Know the formula nλ = dsinθ
Be able to use the formula nλ = dsinθ to calculate n, λ or sinθ
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POLARISATION
YOU MAY HAVE HEARD OF, OR EVEN WORN, POLAROID SUNGLASSES.
THEY ARE PARTICULARLY GOOD AT MAKING THINGS EASIER TO SEE IN BRIGHT SUNLIGHT,
ESPECIALLY WHEN THE SUNLIGHT IS REFLECTED OFF SURFACES SUCH AS SNOW OR ICE, OR OFF THE SEA. ACTUALLY, ‘POLAROID’
IS A GENERAL NAME FOR A TYPE OF SUBSTANCE THAT CAN BLOCK CERTAIN TYPES OF LIGHT. YOU WILL SEE WHAT HAPPENS
TO A BEAM OF LIGHT WHEN IT PASSES THROUGH PIECES OF POLAROID. LATER YOU SHOULD BE ABLE TO EXPLAIN HOW
POLAROID WORKS (NOT JUST WHAT IT DOES).
KEY POINTS
1. Polaroid is a material that blocks photons with some polarisations and allows others through. Polaroid can be used to
select photons of a single plane of polarisation out of a beam of randomly polarised light.
Photons polarised in the same direction as the ‘preferred
direction’ of the polaroid goes through. Their plane of
polarisation is not changed.
Photons polarised at right angles to the ‘preferred direction’ of
the polaroid are completely blocked.
Photons whose plane of polarisation is neither completely in
the same direction nor at right angles to the ‘preferred direction’
have a chance of getting through; but their plane of polarisation
will be in the ‘preferred direction’ of the polaroid. The light
emerging form the polaroid will be less intense that the incident
light.
Figure 3 Example of how polaroid can affect photons with different planes of polarisation. Note: the red dotted
lines show the ‘preferred direction’ of the polaroid.
OTHER POINTS
1. A ray of light is made up of a vast number of photons. We can say that a ray of light is plane polarised. However,
it is the photons that make up the ray that have the property of being polarised.
2. When a photon has its plane of polarisation in line with the preferred direction of polaroid it can pass straight
through; if it is at right angles, the photon will be completely blocked. At ‘in between’ angles, whether the photon
gets through or not is a matter of chance—some will, some won’t; but those that do get through have their plane of
polarisation changed to match the preferred direction of the polaroid. Because not all the photons get through, the
intensity of the light is reduced. (See question 1 below.)
APPLICATIONS OF POLARISATION
1. ‘Polaroid’ sunglasses. By only allowing photons of some polarisations through, the full glare of sunlight is reduced.
2. The signals sent out from radio and television stations are made to be plane polarised. For best reception, aerials
have to be aligned to match the polarisation of the incoming signal.
3. You may see odd patterns in the glass of car windscreens. These are caused by ‘stress polarisation’ of the glass when
it is being made. The process makes some directions in the glass behave differently to others when photons of different
polarisations pass through the glass.
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4. Light from the sky is polarised; bees and other flying creatures can make use of the angle of polarisation to help them
navigate.
5. LCD screens in, for example, digital watches and calculators make the numbers and letters appear and disappear
by using substances that can change their polarising power when a voltage is applied to them.
You can find details of these applications on the web sites listed below.
ABOUT POLARISATION
You do not need to know the details in this section for the Leaving Certificate Physics examination; but it will
help you understand what polarisation is about, and give you a better idea of the nature of light.
1. Photons (or light waves) consist of an electric field (E) and a magnetic field (H).
2. These fields are always changing (oscillating) but always they are at right angles to each other. (They are
perpendicular to one another.)
Figure 1
How the electric
and magnetic fields
of a photon change
Y
Electric field shown in red
X
Magnetic field shown in blue
Direction of travel
This diagram gives you a better
idea of how the electric field
(shown by the red lines)
changes as the photon travels
(from left to right).
3. The fields are also at right angles to the direction of travel of the photon.
4. A plane polarised light wave has photons with their electric fields oscillating in only one plane. See
Figure 2.
Figure 2
Examples of four separate photons with different planes of
polarisation. (You have to imagine that the photons are
coming towards you out of the page)
5. In the light that comes from the Sun or an electric light bulb the planes of the electric (and magnetic) fields
are randomly arranged. See Figure 3.
Figure 3
Example of a beam of light containing four types of photon with different planes of
polarisation. (You have to imagine that the photons are coming towards you out of the
page.) In ordinary unpolarised light, there would be so many ‘arrows’ that the diagram
would just be a dark circle.
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EXPERIMENTS
The main experiment or demonstration you should see is how two pieces of polaroid affect a light beam. When the preferred
direction in the polaroid line up, the light passes straight through. When the preferred directions are at right angles, the
light beam is blocked.
QUESTIONS/PUZZLES
1. Suppose a ray of unpolarised light was shone on one piece of polaroid and then through a second piece as shown
in Figure 4.
Figure 4 Unpolarised light strikes the first piece of polaroid. Any light that gets through hits the second piece. What
would you expect to see if you looked through the two pieces of polaroid and the second piece was slowly rotated?
2. Look at the aerials on your house or flat (or those in your neighbourhood). Which ways are the aerials pointing,
and how are the bars on the aerials arranged? What has the arrangement of the aerials to do with polarisation?
3. If you look at the surface of the sea or a lake in bright sunlight, the glare can be very intense. However, if you
look through polaroid sunglasses, the glare is much less. But if you rotate the sunglasses through 90 degrees, the
glare increases. What do you think this shows about the polarisation of much of the light reflected off the surface
of water?
4. You may know that light behaves as a transverse wave. Sound waves are longitudinal waves. Can you think of a
way of making plane polarised sound waves? Or does the idea of polarisation only apply to transverse waves? Write
down one or two sentences to explain your answer.
5. A physics text book contains the following statement: ‘Light waves are transverse, which means that they vibrate
at right angles to the direction in which they are travelling.’ On your own, or with members of your group, write down
answers to these questions:
(i) Why is it incorrect to say that a ‘light wave’ vibrates?
(ii) What is it about a photon that does change with a wave-like motion?
(iii) Would it be correct to say that a photon vibrates?
(iv) Does anything ‘in’ or ‘about’ light vibrate?
USEFUL WEBSITES
micro.magnet.fsu.edu/primer/lightandcolor/polarizedlightintro.html
micro.magnet.fsu.edu/optics/lightandcolor/polarization.html
micro.magnet.fsu.edu/optics/activities/students/index.html
As its name suggests, the following site has a great deal of information on all sorts of things to do with polarisation
(yes, there really is no ‘www’ in the address): polarization.com/
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