WAVE INTER

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INTERFERENCE
Interference patterns are a direct result of superpositioning.
Antinodal and nodal lines are produced.
These patterns can be enhanced using diffraction gratings, where all waves
pass through each other from multiple point sources.
We also learnt that the path difference for a point on a an antinodal line is
always a factor of a wavelength, , whereas for a nodal line is half a
wavelength, ½.
Antinodal line path difference = n
Nodal line path difference = n½
Where n = order 0, 1, 2, 3, …….
Red: crest meets crest
Or trough meets trough.
Constructive interference

Blue: crest meets a
trough and they cancel
out.
Destructive interference




Can be used to calculate the path difference.
Whole numbers: antinodal lines
Half numbers: nodal lines
5
wavelengths
6
wavelength
s
S1 and S2 are two
coherent sources
All points on a wavefront are in
phase with one another
Waves interfere constructively
where wavefronts meet.
= antinodal lines
2
1
Along the nodal lines,
destructive interference
occurs.
Here antiphase wavefronts
S2
meet.
0
1
2
Wave
Intensity
(Fringes)
n = order number
S1
Young’s Double Slits
A series of dark and
bright fringes on the
screen.
Monochromatic
light, wavelength

Double
slit
Screen
Young’s Double Slit Experiment
THIS RELIES INITIALLY ON
LIGHT DIFFRACTING
THROUGH EACH SLIT.
Where the diffracted light
overlaps, interference
occurs
Light
INTERFERENCE
Double
slit
Diffraction
screen
Some fringes may be
missing where there is a
minimum in the diffraction
pattern
Assuming the sources are coherent
Wave trains AP & BP
have travelled the same
distance
(same number of ’s)
A
P
B
Hence waves arrive
in-phase
CONSTRUCTIVE
INTERFERENCE
(Bright fringe)
Slits
d
L
d = slit separation
dx
n 
L
Screen
x = fringe
separation
Normal light sources emit photons at
random, so they are not coherent.
LASER
LASERS EMIT COHERENT LIGHT
LASER
Example 5:
Monochromatic light from a point source
illuminates two parallel, narrow slits. The centres
of the slit openings are 0.80mm apart. An
interference pattern forms on screen placed
2.0m away. The distance between two adjacent
dark fringes is 1.2mm.
Calculate the wavelength, , of the light used.
Example 5:
Monochromatic light from a point source illuminates two parallel, narrow slits. The
centres of the slit openings are 0.80mm apart. An interference pattern forms on screen
placed 2.0m away. The distance between two adjacent dark fringes is 1.2mm.
Calculate the wavelength, , of the light used.
SOLUTION:
The distance to the screen (2.0m) is large compared with the fringe spacing (1.2mm). The
approximation formula can be used.
n = dx/L [n = 1 because the fringe spacing is being calculated]
= (8.0 x 10-4 x 1.2 x 10-3) / 2.0
= 4.8 x 10-7 m

Decide which points are Constructive
interference and which are Destructive
interference?

In phase
Out of phase
By 180 deg (half
a wavelength)



Quantum Physics.
http://www.doubleslitexperiment.com/


Double slit animation.
http://www.colorado.edu/physics/2000/schro
edinger/two-slit2.html
dx
n 
L
PD= m λ
Two point sources, 3.0 cm apart, are generating periodic waves in phase.
A point on the third antinodal line of the wave pattern is 10 cm from one
source and 8.0 cm from the other source. Determine the wavelength of
the waves.
Two point sources are generating periodic waves in phase. The
wavelength of the waves is 3.0 cm. A point on a nodal line is 25 cm from
one source and 20.5 cm from the other source. Determine the nodal line
number.
The Diffraction Grating: This is a piece of glass with tiny slits
made in it to produce small point sources.
A formula can be used to relate to the interference pattern
produced by a particular diffraction grating.
dsin
= n
(Where n = 0, 1, 2, 3 …….)
Often N, the number of slits per metre, or slits per
centimetre is given. The slit spacing d is related to N by:
d = 1/N

A
C

Monochromatic light
B
Grating
1
d
number of lines per metre
d sin   n
 
red light  700 nm, violet light  400 nm
Several spectra will be seen,
the number depending upon
the value of d
Second Order maximum, n = 2
First Order maximum, n = 1
White Central maximum, n = 0
First Order maximum, n = 1
Grating
Second Order maximum, n = 2
screen
n=3
n=2
n=1
n=0
Note that higher
orders, as with 2 and
3 here, can overlap
Note that in the
spectrum produced
by a prism, it is the
blue light which is
most deviated
grating
Example: Light from a laser passes through a diffraction grating of 2000
lines per cm. The diagram below shows the measurement made.
0 order
laser

0.5m
Grating
2m
2nd order
Calculate the wavelength of the light.
SOLUTION:
sin = 0.5/2
Slit spacing d = 1/N
= 1/200000
= 0.250
= 5.00 x 10-6m
 = dsin/n
= (5.00 x 10-6 x 0.250) / 2
= 6.25 x 10-7m

http://webphysics.ph.msstate.edu/javamirror
/ipmj/java/slitdiffr/index.html
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