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4.3 Wave characteristics
A reminder - Wave fronts
Wave fronts highlight the part of a wave
that is moving together (in phase).
= wavefront
Ripples formed by a
stone falling in water
Rays
Rays highlight the direction of energy
transfer.
Wave intensity
Wave intensity
This is defined as the amount of energy per
unit time flowing through unit area
It is normally measured in W.m-2
Wave intensity
For example, imagine
a window with an
area of 1m2. If one
joule of light energy
flows through that
window every second
we say the light
intensity is 1 W.m-2.
Intensity at a distance from a light source
Can you
follow Mr
Porter
please?
Intensity at a distance from a
light source
I = P/4πd2
where d is the distance from the light source
(in m) and P is the power of the light
source(in W)
Intensity at a distance from a
light source
I=
2
P/4πd
d
Data booklet
Iα
-2
x
Intensity and amplitude
Intensity and amplitude
The intensity of a wave is proportional to
the square of its amplitude
I α A2
(or I =
2
kA )
Intensity and amplitude
This means if you double the amplitude of a wave,
its intensity quadruples!
I=
2
kA
If amplitude = 2A,
new intensity = k(2A)2
new intensity = 4kA2
Surfers know this!
4.3 Wave Intensity video
4.3 Wave Intensity worksheet
Superposition
Principle of superposition
When two or more waves meet, the
resultant displacement is the sum of the
individual displacements
Constructive and destructive
interference
When two waves of the same frequency
superimpose, we can get constructive interference
or destructive interference.
+
=
+
=
Superposition
In general, the displacements of two (or
more) waves can be added to produce a
resultant wave. (Note, displacements can be
negative)
4.3 Superposition
Let’s try adding some waves!
Polarized waves (transverse only)
• Vibrations lie in the same plane
Polarized light
Often a plastic called
“Polaroid” discovered by
a 19 year-old Harvard
undergradutae called
Edwin Land in 1928
Polarized light
50% goes through
(important)
Polarized light
Polarization by reflection
Brewster angle
• In 1812, Sir David Brewster found
experimentally that the reflected ray is
100% polarized when the angle between the
reflected ray and the refracted ray is 90°
Brewster’s angle tanθB = n2/n1
If ray is incident from air, n1 = 1, so tanθB = n2
normal
η = n1
η = n2
θB
Completely
polarized
reflected ray
You don’t need to know
or use this formula!
Calculate Brewster’s angle for
light incident on water (η = 1.33)
Calculate Brewster’s angle for
light incident on water (η = 1.33)
tanθB = n2/n1 = 1.33/1 = 1.33
θB = 53.1º
You don’t need to know
or use this formula!
Polarisation by dispersion!
Polarizers and analysers
• A polarizer (like polaroid) can be used to
polarize light
Polarizers and analysers
• Another polarizer can also be used to
determine if light is polarized. It is then
called an analyser.
Malus’ Law
• The intensity of polarised light that passes
through a polarizer is proportional to the
square of the cosine of the angle between
the electric field of the polarized light and
the angle of the polarizer!
Malus’ law
I = Iocos2θ
Io
Iocos2θ
Optical activity
• Some substances can change the plane of
polarized light. We say they are optically
active
Optical activity
Sugar solution is optically active. The
amount of rotation of the plane of
polarization depends on the concentration of
the solution.
Stress analysis
Some substances, not normally optically
active, become optically active if subject to
stresses.
Stress analysis
Analysis of the patterns reveals how the
stress varies in the material.
4.3 Polarisation worksheet