Chapter 28
Interference and
Diffraction of Waves
Interference


Light waves interfere with each other
much like mechanical waves do
All interference associated with light
waves arises when the
electromagnetic fields that constitute
the individual waves combine
Interference and Coherent Light Source
Any situation in which two or more waves overlap in space
Principle of Superposition
Conditions for Interference

For sustained interference between
two sources of light to be observed,
there are two conditions which must
be met
• The sources must be coherent

They must maintain a constant phase with
respect to each other
• The waves must have identical
wavelengths
Producing Coherent Sources




Light from a monochromatic source is
allowed to pass through a narrow slit
The light from the single slit is allowed to
fall on a screen containing two narrow slits
The first slit is needed to insure the light
comes from a tiny region of the source
which is coherent
Old method
Coherent light sources by splitting
3rd
2nd
1st
0th
Huygen’s principle: Each point on a wavefront acts as a new
Source of identical waves.
Producing Coherent Sources,
cont


Currently, it is much more common
to use a laser as a coherent source
The laser produces an intense,
coherent, monochromatic beam over
a width of several millimeters
Interference and Diffraction of Light Wave
Christiaan Huygens
(1629 -1695)
Thomas Young
(1773 -1829)
His double slit experiment proved wave-like
nature of light.
Let’s see the interference of water ripples.
http://www.falstad.com/ripple/
Young’s Double Slit Experiment



Thomas Young first demonstrated
interference in light waves from two
sources in 1801
Light is incident on a screen with a
narrow slit, So
The light waves emerging from this
slit arrive at a second screen that
contains two narrow, parallel slits, S1
and S2
Young’s Double Slit Experiment,
Diagram


The narrow slits,
S1 and S2 act as
sources of waves
The waves
emerging from the
slits originate from
the same wave
front and therefore
are always in
phase
Resulting Interference Pattern




The light from the two slits form a
visible pattern on a screen
The pattern consists of a series of
bright and dark parallel bands called
fringes
Constructive interference occurs
where a bright fringe occurs
Destructive interference results in a
dark fringe
Interference Patterns


Constructive
interference occurs
at the center point
The two waves
travel the same
distance
• Therefore, they
arrive in phase
Interference Patterns, 2


The upper wave has
to travel farther than
the lower wave
The upper wave
travels one
wavelength farther
• Therefore, the waves
arrive in phase

A bright fringe occurs
Interference Patterns, 3



The upper wave
travels one-half of a
wavelength farther
than the lower wave
The trough of the
bottom wave
overlaps the crest of
the upper wave
This is destructive
interference
• A dark fringe occurs
Young’s Double Slit Experiment (1802)
Whenever two portions of the same light arrive at the eye
by different routes, either exactly or very nearly in the
same direction, the light becomes most when the
difference of the routes is any multiple of a certain length,
and the least intense in the intermediate state of
interfering portions; and this length is different for light
of different colour.
T. Young from a paper to the Royal Society in 1802
r1
•P
s1
r2
s2
|r1 – r2| = 0, l, 2l, 3l, …, ml (m: integer)  Constructive Int.
|r1 – r2| = l/2, 3l/2, 5l/2, …, (2m+1)l/2  Destructive Int.
l
● P
s1
q
d
s2
dsinq
Along the center line, it is obvious that the distances to
two sources are identical.  |r1-r2| = 0 and constructive int.
|r1 - r2| = dsinq = ml
= (2m + 1)l/2
Constructive Int.
Destructive Int.
Approximation valid when d << r!!
dsinq =
ml (0, ±l, ±2l, …)
Constructive
(2m+1)l/2 (±l/2, ±3l/2,…)
Destructive
d(x/h) = ml  x = (h/d)ml for constructive int.
3rd
2nd
q
d
h
st
1x
0th
1st
2nd
3rd
Ex.28.1 In a certain double slit experiment, the slit separation is
0.050 cm. The slit-to-screen distance is 100 cm. When blue light
is used, the distance from the central fringe to the fourth-order
bright fringe is 0.36 cm. Find the wavelength of the blue light.
d = 0.05 cm
h = 100 cm
x = 0.36 cm
m = 4 constructive
d (x/h) = ml
l = (d/m)(x/h)
= (0.05/4)(0.36/100)
= 4.5 x 10-5 cm
= 450 nm
However, this analysis based on the assumptions that
the two light sources have exactly the same frequency
and they are absolutely in phase all the time.
Two identical monochromatic light source:
Same frequency and constant phase relation (could be in-phase)
Coherent Light Source