STAGE 2 PHYSICS
READING
Electricity and Magnetism
Key Ideas pg
pg
Interference A
Key Ideas
Intended Student Learning
Coherent Wave Sources
‘Coherent’ wave sources are wave sources that
maintain a constant phase relationship with each other.
They must therefore have the same frequency.
Describe what is meant by two wave sources being in
phase or out of phase.
‘Monochromatic’ light is light composed of a single
frequency.
Give a qualitative explanation of why light from an
incandescent source is neither coherent nor
monochromatic.
Interference
In the region where two or more electromagnetic
waves overlap, the resultant electric and magnetic
fields at a point are the vector sums of their separate
fields. This is an example of the principle of
superposition.
In the region where two or more electromagnetic
waves overlap, the resultant electric and magnetic
fields at a point are the vector sums of their separate
fields. This is an example of the principle of
superposition.
In the region where two or more electromagnetic
waves overlap, the resultant electric and magnetic
fields at a point are the vector sums of their separate
fields. This is an example of the principle of
superposition.
Describe constructive and destructive interference in
terms of the principle of superposition.
Two-source Interference
For two monochromatic sources in phase, the waves at
a point some distance away in a vacuum:
 constructively interfere when the path difference from
the sources to the point is m
Perform a geometrical construction to identify the
locations in two dimensions of the lines of maximum
and minimum amplitude due to the interference of light
from two wave sources of the same frequency.
 destructively interfere when the path difference from
the sources to the point is  m  1 2  
where m is an integer and  is the wavelength.
Explain the maximum and minimum amplitudes in
terms of constructive and destructive interference.
Explain the maximum and minimum amplitudes in
terms of constructive and destructive interference.
Diffraction
The spreading out of plane waves as they pass
through an opening is an example of diffraction. This is
most noticeable when the opening is comparable in
size with the wavelength of the waves.
Describe without detailed explanation the main feature
of the diffraction of light by a narrow slit, where the
width of the slit is about the same size as the
wavelength.
Two-slit Interference
Interference between light diffracted by two narrow slits
can be produced by illuminating the slits with light from
a laser or by passing light from a monochromatic
source through a single slit before illuminating the
double slits.
Explain why a single slit is used before a double slit for
two-slit interference when the light source used is not
coherent.
Describe how two-slit interference is produced in the
laboratory.
Describe how two-slit interference is produced in the
laboratory.
Sketch a graph of the intensity distribution for two-slit
interference of monochromatic light. (Consider only
cases where the slit separation is much greater than
the width of the slits.)
Explain the bright fringes of a two-slit interference
pattern in terms of constructive interference, and the
dark fringes in terms of destructive interference.
Derive d sin   m for two-slit interference, where d
is the distance between the slits and  is the angular
position of the mth maximum.
Solve problems involving the use of d sin   m and
 y   L d .  y is the distance between adjacent
minima or maxima on the screen and L is the slit-toscreen distance.
Determine the wavelength of monochromatic light from
measurements of the two-slit interference pattern.
The Nature of Light
For more than three hundred years, the nature of light has been the subject of arguments between
scientists. Some have thought that light behaves as waves, others that light behaves as particles.
Sir Isaac Newton (1642-1727) believed that light consisted of particles or corpuscles.
The Dutch scientist, Christian Huygens (1629-1695), agreed with the wave nature of light and was
able to explain reflection and refraction by using the properties of waves. However, none of these
scientists had enough influence to seriously challenge people's belief in Newton's theory of light as
particles, until Thomas Young carried out his experiments with light.
Thomas Young
Thomas Young carried out many investigations into different areas of science. In 1800 he published a
paper on sound and light which was presented to the Royal Society.
This paper provided experimental evidence which could only be explained by the wave theory of
light.
However, no-one appreciated the importance of his discoveries until Augustin Fresnel repeated
many of them 14 years later.
Interference of Waves
When two waves meet their
amplitudes add together giving a
resultant wave at the point where
they meet.
If their amplitudes are both positive a
larger wave results. This is called
constructive interference or
reinforcement.
If the amplitude of one wave is
positive but the other is negative, the
amplitude of the waves is reduced.
This is called destructive
interference.
Conditions for Constructive Interference
Constructive interference occurs between two waves, when the
path difference is always a whole number of wavelengths.
Path difference for constructive interference = mλ where m = 0,
1, 2, 3, ...
Conditions for Destructive Interference
Destructive interference occurs; the path difference is always a
whole number of wavelengths plus half a wavelength.
Path difference for destructive interference = mλ + λ/2 where m =
0, 1, 2, 3,
When the amplitudes of two waves are equal, but one is positive
and the other negative, the resultant amplitude will be zero. The
two waves will have cancelled each other out completely. This is
called annulment.
Diffraction
Diffraction is the spreading of waves
around an obstacle.
A slit can be thought of as a narrow
space between two obstacles.
Huygen’s Principle
“Every point on an advancing wavefront is the source of a secondary circular wavelet. The new
wavefront is the tangent to these circular wavelets”
Huygen suggested that the behavior of waves can be explained by considering that each point on a
wave front produces semi-circular wavelets and a new wave front is the result of the addition of all
the wavelets.
Monochromatic and Coherent Light
Monochomatic light is light of one wavelength only. Waves are coherent if there is a constant phase
difference between them,
i.e. if at one point in time the phase difference between the waves is λ/2 then the phase difference
continues to be λ/2 as the waves advance.
This can only occur when the waves have the same frequency
A source of visible light such as the sun, electric light globes, fluorescent light globes, a candle, etc,
contain large numbers of different atoms, all of whose electrons are vibrating independently. All
these different atoms produce light waves of different wavelengths and in different phases. The light
is therefore not monochromatic and not coherent.
It is very difficult to see diffractions patterns unless the light is coherent.
Young’s Double Slit Experiment
Thomas Young was the first person to discover a method of producing two sources of light which
would emit coherent waves.
When the light arrives at the screen, alternating, relatively wide, bright lines and dark lines are
seen. The bright and dark bands are called fringes. A bright fringe may be called a maximum
a dark fringe may be called a minimum.
P is the position of the centre of the first bright fringe, or maximum, adjacent to the central
maximum, i.e. the first order bright fringe
•
NP is equal to S1P, i.e. the path difference (PD) is 0 x λ
•
S2N is the PD between the waves from S1 to P and the waves from S2 to P
•
 is the angle OMP and in reality is very small
•
from the geometry, angle S1S2N is also equal to 
•
angle S1NS2 is very close to a right-angle because  is very small
•
sy the distance from the centre of the central maximum to the centre of the first
adjacentmaximum at P.
Derivation of dsin  = mλ and y = λL/d
Example Question
1. In a double slit apparatus, the distance between the two slits is 5.0 x 10-5 m and the distance
from the slits to the screen is 30 cm.
a. Orange light of wavelength 589 nm is shone into the apparatus. Find the fringe
separation.
b. Find the distance from the central bright fringe to the third dark fringe.
c. Light of a different colour is shone into the apparatus at the same time as the
orange light. It is found that the second bright band of the new colour coincides with
the third dark fringe of the orange light. Find the wavelength of the new colour.