UNIT 5: INTERFERENCE OF LIGHT WAVES
Key unit competence: Perform experiment for interference of light
waves.
Unit Objectives:
By the end of this unit I will be able to;
◊ explain the concept of wave interferences and their applications in our daily
life.◊ explain the interaction of electromagnetic radiations with the earth.
Introductory Activity
Observe the diagram below and answer the questions that follow
M,
a) Why do you think there are Minimum (min) and Maximum (Max)
regions as indicated on the screen?
b) Relating part a) and part b), what do you think lead to the formation
of the patterns as indicated in b)
c) What scientific phenomena, that explains the figure shown above?
d) Do you think the process indicated in the figure is applicable andimportant in the world we live in?
5.0. INTRODUCTION
Sun is a nuclear fireball spewing energy in all directions. The light that
we see it simply one part of the energy that the Sun makes that our eyes
can detect. When light travels between two places (from the Sun to the
Earth or from a flashlight to the sidewalk in front of you on a dark night),
energy makes a journey between those two points. The energy travels in the
form of waves (similar to the waves on the sea but about 100 million times
smaller)—a vibrating pattern of electricity and magnetism that we call
electromagnetic energy. If our eyes could see electricity and magnetism, we
might see each ray of light as a wave of electricity vibrating in one direction
and a wave of magnetism vibrating at right angles to it. These two waveswould travel in phase and at the speed of light.
5.1. NATURE OF ELECTROMAGNETIC WAVES
Electromagnetic waves are transverse waves that transfer electrical and
magnetic energy. An electromagnetic wave consists of vibrating electric
and magnetic fields that move through space at the speed of light. In other
words electromagnetic waves have electric and magnetic fields varyingperpendicularly as shown on Fig.5.1.
5.1.1 Producing electromagnetic waves
Electromagnetic waves are produced by charged particles and every charged
particle has an electric field surrounding it. The electric field produces
electric forces that can push or pull on other particles.
When a charged particle moves, it produces a magnetic field which exerts
magnetic forces that act on certain materials.
When this charged particle changes its motion, its magnetic field changes
and causes the electric field to change. When one field vibrates, so does the
other and the two fields constantly cause each other to change and this
produces an Electromagnetic wave.
Many properties of electromagnetic waves can be explained by a wave model
and some other properties are best explained by a particle model. Both a
wave model and a particle model are needed to explain all of the properties
of electromagnetic waves and in particular light.
5.1.2 Electromagnetic Radiation
Water waves transmit energy through space by the periodic oscillation of
matter (the water). In contrast, energy that is transmitted, or radiated,
through space in the form of periodic oscillations of electric and magnetic
fields is known as electromagnetic radiation. In a vacuum, all forms of
electromagnetic radiation—whether microwaves, visible light, or gamma
rays—travel at the speed of light (c), this is about a million times faster
than the speed of sound.
All forms of electromagnetic radiation consist of mutually perpendicular
oscillating electric and magnetic fields. Because the electromagnetic
radiations have same speed (c), they differ only in their wavelength andfrequency.
5.1.3 Electromagnetic spectrum
When you tune your radio, watch TV, send a text message, or pop popcorn
in a microwave oven, you are using electromagnetic energy. You depend on
this energy every hour of every day. Without it, the world you know would not exist.
Electromagnetic energy travels in waves and spans a broad spectrum from
very long radio waves to very short gamma rays. The human eye can only
detect only a small portion of this spectrum called visible light. A radio
detects a different portion of the spectrum, and an x-ray machine uses yetanother portion.
Generation, properties and uses of those waves are summarized in the table
below:
ACTIVITY 5-1: Spectrum of Electromagnetic Waves
Aim: In this activity, you will investigate the spectrum of visible light
Materials needed: a white sheet of paper, a glass prism and colored
pencils
Shine a light through a prism so that the light leaving the prism falls
on an unlined piece of paper. What colours do you see? As you hold the
prism and light steady, your partner will use coloured pencils to draw
the colours on the piece of paper. Switch places with your partner. Again,
trace the colours you see onto the piece of paper.
◊ What colours do you see on the paper? What is the order of the colours?
◊ Is it difficult to see where one colour ends and the next begins?
◊ Did the order of the colours on the paper ever change?
◊ The term spectrummeans a range. How do you think this term is relatedto what you observed?
5.1.4 Radiation Interaction with the Earth
Radiation that is not absorbed or scattered in the atmosphere can reach
the earth and interact with its surface. There are three forms of interaction
that can take place when energy strikes, or is incident upon the surface.
These are: absorption (A); transmission (T); and reflection (R).
Reflection: Reflected light is perceived by our eye as colour, e.g. chlorophyll
in plants reflects green light. All colours of the visible spectrum are absorbed.
Absorption: The incident energy might not get reflected or transmitted but
is transformed into another form, such as heat or absorbed by chlorophyll
in the process of photosynthesis.
Transmission: When energy propagates through a medium, what is
not absorbed or reflected, will be transmitted through. For instance, an
ultraviolet filter on a camera absorbs UV rays but allows the remaining
energy to expose the film. Changes in density can also slow the velocity of
light resulting in refraction such as dispersion through a prism.
5.1.5 Radiation Interaction with the Atmosphere
The Earth’s atmosphere acts as a filter to remove radiations such as cosmic
rays, gamma rays, X-rays, UV rays, and large portions of the electromagnetic
spectrum through the process of absorption and scattering by gases, water
vapour, and particulate matter (dust).
Scattering occurs when particles or large gas molecules present in the
atmosphere cause the electromagnetic radiation to be redirected from its
original path. There are three types of scattering which take place: Rayleigh
Scattering, Mie Scattering, Non-selective Scatter.
Rayleigh scattering refers to the scattering of light off by the molecules of
air. It can be extended to scattering from particles of sizes up to about one
tenth of the wavelength of the light. It is Rayleigh scattering of white lightby the molecules of the air which gives us the blue sky.
Mie scattering is caused by pollen, dust, smoke, water droplets and other
particles in the lower portion of the atmosphere. It occurs when the particles
causing the scattering are larger than the wavelengths of radiation in
contact with them. Mie scattering is responsible for the white appearanceof the clouds, as seen below.
Non-Selective Scattering occurs when the particles are much larger than
the wavelength of the radiation. Water droplets and large dust particles can
cause this type of scattering and cause fog and clouds to appear white to our
eyes because blue, green, and red light are all scattered in approximately
equal quantities (blue+green+red light = white light).
5.1.6 Atmospheric Absorption of electromagnetic waves
In addition to the scattering of EM radiation, the atmosphere also absorbs
electromagnetic radiation. The three main constituents of atmosphere
which absorb parts of solar radiation are Ozone, Carbon dioxide, and Water
Vapour.
Ozone serves to absorb the harmful ultraviolet radiations from the sun.
Without this protective layer in the atmosphere, our skin would burn whenexposed to sunlight. Ultraviolet rays can also cause skin cancer to people.
Carbon Dioxide absorbs the far infrared portion of the spectrum which is
related to thermal heating and results in a ‘greenhouse’ effect.
Water Vapour absorbs energy depending upon its location and concentration,and forms a primary component of the Earth’s climatic system.
5.2. CONDITIONS FOR INTERFERENCE WITH TWO
SOURCES OF LIGHT
When two waves of exactly same frequency (coming from two coherent
sources) travel in a medium, in the same direction simultaneously then due
to their superposition, at some points intensity of light is maximum while
at some other points intensity is minimum. This phenomenon is called
Interference of light.
There are two types of interference: constructive interference and
destructive interference.
A constructive interference is produced at a point when the amplitude of
the resultant wave is greater than that of any individual wave.
A destructive interference is produced at a point when the amplitude of the
resultant wave is smaller than that of any individual wave.
Conditions for interference
When waves come together they can interfere constructively or destructively.
To set up a stable and clear interference pattern, two conditions must be met:
• The sources of the waves must be coherent, which means they emit
identical waves with a constant phase difference.
• The waves should be monochromatic - they should be of a singlewavelength.
5.3. PRINCIPLE OF SUPERPOSITION
The principle states that when two or more than two waves superimpose
over each other at a common particle of the medium then the resultantdisplacement
of the particle is equal to the vector sum of the displacements
Consider two waves given as:
EXAMPLES
1. Two waves traveling in opposite directions produce
a standing wave. The individual wave functions are
(C) What is the maximum value of the position in the simple harmonic
motion of an element located at an antinode?
Answer
The maximum position of an element at an antinode is the amplitude ofthe standing wave, which is twice the amplitude of the individual traveling waves:
where we have used the fact that the maximum value of
5.4. INTERFERENCE PATTERN OF TWO COHERENT
POINT SOURCES OF LIGHT
The sources of light which emit continuous light waves of the same
wavelength, same frequency and are in same phase (or have a constant
phase difference) are called coherent sources. Two coherent sources areproduced from a single source of light by using Young’s double slits.
From the Fig. 13.7. S1 and S2 are coherent sources and show interference
as light passes through two slits. It also shows the appearance of the
interference pattern on a screen placed in the path of the beam. You can
see the maxima and minima and the way in which the intensity changes.
Changing the wavelength of the light, the separation of the slits or the
distance of the slits from the screen will all give changes in the separation
of the maxima in the interference pattern.
5.5. YOUNG'S DOUBLE-SLIT EXPERIMENT
Monochromatic light (single wavelength) falls on two narrow slits S1
and S2 which are very close together and act as two coherent sources.
When waves coming from two coherent sources superimpose on each other,an interference pattern is obtained on the screen. In Young’s double slit
experiment alternate bright and dark bands are obtained on the screen.These bands are called Fringes.
Following points must be noted and observed in the above experiment:
• Central fringe is always bright, because at central position,
the path difference
• The fringe pattern obtained due to a slit is more bright than that due
to a point.
• If the slit widths are unequal, the minima will not be completly dark.
For very large slit width, uniform illumination occurs, i.e. bright and
dark fringes are not formed.
• If one slit is illuminated with red light and the other slit is illuminated
with blue light, no interference pattern is observed on the screen.
• If the two coherent sources consist of object and its reflected image,
the central fringe is dark instead of bright one.
Calculation of fringe separation/fringe width
Consider two coherent sources (slits) S1 and S2
separated by distance d.
The distance D from the plane of slits to the screen is much greater than d.
Consider a wave from S1 that meets another wave from S2 at point P.
Example
1. A viewing screen is separated from a double-slit source by 1.2 m. The distance
between the two slits is 0.030 mm. The second-order bright fringe (m = 2) is 4.5 cm
from the center line.
(a) Determine the wavelength of the light.
(b) Calculate the distance between adjacent bright fringes.Solution
• Increasing the width of the slits increases the intensity of waves and
fringes become more blurred.
Application Activity 5.2
1. What is the necessary condition on the path length difference between
two waves that interfere (a) constructively and (b) destructively?
2. If Young’s double-slit experiment were performed under water, how
would the observed interference pattern be affected?
3. In Young’s double-slit experiment, why do we use monochromatic
light? If white light is used, how would the pattern change?
4. The distance between the two slits is 0.030 mm. the second-order
bright fringe (m = 2) is measured on a viewing screen at an angle of
2.150 from the central maximum. Determine the wavelength of the light.
5. A 2-slit experiment is set up in which the slits are 0.03 m apart.
A bright fringe is observed at an angle 10° from the normal. What is
wavelength of electromagnetic radiation being used?
6. In Young’s double slit experiment the separation between the 1st and
5th bright fringes is
. When the wavelength used is 
The distance from the slits to screen is 0.8 m. Calculate the separationof the slits
5.6. INTENSITY DISTRIBUTION OF FRINGE PATTERN
So far we have discussed the locations of only the centers of the bright and
dark fringes on a distant screen. We now direct our attention to the intensity
of the light at other points between the positions of maximum constructive and
destructive interference. In other words, we now calculate the distribution oflight intensity associated with the double-slit interference pattern.
Again, suppose that the two slits represent coherent sources of sinusoidal
waves such that the two waves from the slits have the same angular
frequency w and a constant phase difference
. The total magnitude of
the electric field at point P on the screen is the vector superposition of the
two waves. Assuming that the two waves have the same amplitude E0, we
can write the magnitude of the electric field at point P due to each waveseparately as;
Finally, to obtain an expression for the light intensity at point P, the
intensity of a wave is proportional to the square of the resultant electricfield magnitude at that point;
Note that the interference pattern consists of equally spaced fringes of
equal intensity. Remember, however, that this result is valid only if theslit-to-screen distance D is much greater than the slit separation d.
Application Activity 5.3
1. In a double slit interference experiment, the distance between the
two slits is 0.0005m and the screen is 2 m from the slits. Yellow
light from a sodium lamp is used and it has a wavelength of 5.89 ×
10-7 m. Show that the distance between the first and second fringes
on the screen is 0.00233 m.
2. With two slits are spaced 0.2 mm apart, and a screen at a distance of
D = 1 m, the third bright fringe is found to be displaced h = 7.5mm from
the central fringe. Show that the wavelength,
, of the light used is
5 × 10–7 m.
3. Two radio towers are broadcasting on the same frequency. The
signal is strong at A, and B is the first signal minimum. If d = 6.8 km,
L = 11.2 km, and y = 1.73 km, what is the wavelength of the radiowaves to the nearest meter?
4. Water waves of wavelength of 5.44 m are incident upon a breakwater
with two narrow openings separated by a distance 247 m. To the
nearest thousandth of a degree, what is angle corresponding to thefirst wave fringe maximum?
UNIT SUMMARY
Nature of electromagnetic waves
Electromagnetic waves are transverse waves that transfer electrical and
magnetic energy.
In other words electromagnetic waves have electric and magnetic fields
varying perpendicularly.
Producing electromagnetic waves
Electromagnetic waves are produced by charged particles and every charged
particle has an electric field surrounding it. The electric field produceselectric forces that can push or pull other particles.
Electromagnetic Radiation
All forms of electromagnetic radiation consist of perpendicularly oscillating
electric and magnetic fields. Various kinds of electromagnetic radiations
have the same speed (c). They differ only in wavelength and frequency.
Electromagnetic energy travels in waves and spans a broad spectrum
from very long radio waves to very short gamma rays. This is called
electromagnetic spectrum.
From memory you should be able to list the parts in order of energy (relate
how that relates to frequency and wavelength) and know how they are
produced, detected and their dangers and uses - a rough idea of their
approximate wavelength is also useful!
Radiation Interaction with the Earth
Radiation that is not absorbed or scattered in the atmosphere can reach
and interact with the Earth’s surface. There are three forms of interaction
that can take place when energy strikes, or is incident upon the surface.
These are: absorption (A), transmission (T) and reflection (R).
Radiation Interaction with the Atmosphere
The Earth’s atmosphere acts as a filter to remove radiation such as cosmic
rays, gamma rays, X-rays, UV rays and large portions of the electromagnetic
spectrum through the process of absorption and scattering by gases, water
vapour and particulate matter (dust).
Atmospheric Absorption of electromagnetic waves
In addition to the scattering of EM radiation, the atmosphere also absorbs
electromagnetic radiation. The three main constituents which absorb
radiation are Ozone, Carbon Dioxide and Water Vapour.
Conditions for interference to occur
• The sources of the waves must be coherent, which means they emit
identical waves with a constant phase difference.
• The waves should be monochromatic - they should be of a single
wavelength.
Principle of superposition
The principle states that when two or more than two waves superimpose
over each other at a common particle of the medium then the resultantdisplacement (y) of the particle is equal to the vector sum of the displacements
Double-slit experiment
Monochromatic light (single wavelength) falls on two narrow slits S1
and S2 which are very close together acts as two coherent sources, when
waves coming from two coherent sources superimposes on each other, an
interference pattern is obtained on the screen
A bright fringe is obtained when the path difference is a whole number ofwavelength.
