Wave Terminology
1
T
f
1
and f 
T
Phase Shift
Simple Harmonic Motion
Let the vertical displacement be represented by y then
y  A sin 
and the horizontal displacement would be
x  A cos 
Combining both vertical and horizontal
displacements yields:
x 2  y 2  A2 cos 2   A2 sin 2 

x 2  y 2  A2 cos 2   sin 2 

But cos 2   sin 2   1; therefore
x 2  y 2  A2
So these two wave equations
y  Asin  and x  A cos 
represent the components of circular motion in the y
and x directions.
Electromagnetic Theory
The Universal Wave Equation
d
t
substituting  (wavelengt h) for d and T (period) for t
v
as T 
v

T
1
then v becomes;
f
 f the Universal Wave Equation
for light v  c 

T
 f
Measuring the Speed of Light
The Spectrum
Applications Of E-M Waves
Properties of Waves
Rectilinear Propagation of light
Light travels in straight lines. A light particle could
surely travel in straight lines but what about waves?
Straight waves:
Straight waves could
be considered to be
moving in straight
lines but not all waves
are straight.
In circular waves or
any waves that are not
straight, each point on
the wavefront could
be considered to be moving straight
(consider what a surfboard would do on these waves).
Huygen’s Principle:
Every point on wavefront can be considered as a
point source of tiny secondary wavelets that spread
out in front of the wave at the same speed as the
wave itself. The surface envelope, tangent to all the
wavelets, constitutes the new wavefront.
Reflection:
Wavefronts would reflect at these barriers as shown
following the law of reflection (θi = θr and both the
incident and reflected rays lay in the same plane) but
would particles behave the same way?
Refraction:
Light changes
speed upon
encountering a
new medium
which produces
an accompanying
change in
wavelength.
What happens to the frequency of the wave when the speed
changes at a medium boundary?
See how much easier it is to represent refraction with
just rays and without all those wavefronts.
Would particles refract? That is would they change
direction if they met a faster or slower medium at any
angle?
Newton thought so…but there was one problem that
came about when Foucault that the speed of light was
less in certain optically dense mediums such as water.
This was exactly the opposite result that Newton was
counting on.
Recall that the index of refraction is a measure of the
optical density of a transparent medium.
n
c
vmedium
where n is the index of refraction
c is the speed of light in a vacuum (air)
and vmedium is the speed of light in the particular
medium of study.
Table 10.2 lists some specific indices of refraction.
Snell’s Law:
Partial Reflection-Partial Refraction
Waves do this and so does light, just look at your
reflection in a window. Newton had his own theory
of how particles could either reflect or refract at a
boundary…it was called “the theory of fits.”
Dispersion
Dispersion is the separation of white light into
component colours (wavelengths) because of the
differential refraction of each wavelength at each
boundary. Each colour could be assigned a separate
index of refraction to describe how it behaves at a
medium boundary.
So what is white light?
Diffraction
Diffraction is the bending of waves, usually when
they encounter obstacles.
Waves such as sound diffract.
Water waves also diffract. In this case they diffract
when they pass through a hole (aperture) in an
obstacle.
To explain why waves diffract we need to use
Huygen’s Principle of wavelets. Will particles
diffract at the edge of an obstacle the way that these
waves do?
What factors affect the amount of wave diffraction?
Long wavelengths diffract more than short and
narrow slits cause more diffraction than wider ones.
Particles do not diffract but Newton noted that
neither did light. Why did light not appear to diffract
at the time of Newton? Today we can easily verify
that light does actually diffract the way that sound
does. One way to show this is by observing the way
that light interferes at special apertures the way that
sound does.