EM waves from a TV tower are perfectly polarized – the Electric
field has a very well defined direction, which stays always the same.
In contrast, the light coming from the Sun or from a light bulb is
unpolarized.
What does it mean unpolarized? Does not the electric field have
some direction?
It certainly does at every instant. BUT this direction does not stay
constant and changes very rapidly and randomly.
So, after averaging over any reasonable time interval, you do not find
any particular polarization!
polarized
unpolarized
The frequency of light is about 5×1014 Hz, which means 5×1014 wave
crests per second. If the polarization changes once every 500 crests it
will still be 1012 times per second. Too fast for us to detect!
Any way to make a polarized wave (light) out of unpolarized wave?
Yes, but it is going to cost us some intensity loss… (No free meals…)
We can use a polarizer - a piece of material, whose molecular or crystal
structure has a preferred direction called the transmission axis.
A polarizer
 “decomposes” the wave into a “proper” component with the electric
field, E , parallel to the transmission
axis, which passes through, and a

“wrong” component with
totally absorbed.
E perpendicular to the transmission axis, which gets
 θ

E0
E
The magnitude of the proper
component of the electric field:
z
E = E0 cos θ
Intensity of the wave is
proportional to the square of
the amplitude
S~E
2
S = S 0 E 2 / E02 = S 0 cos 2 θ
transmission axis
Law of Malus
In an unpolarized wave, the angle θ is changing randomly.
Therefore, after passing through a polarizer the average intensity is
S = S 0 cos θ = S 0 / 2
2
The light gets polarized, but we
lose 1/2 of its intensity...
If the axis of a polarizer is set at θ = 90° to the axis of polarization
cos θ = 0
no light is passing through!
A system of two crossed polarizers never lets any light through.
Whatever passes through the first one is blocked by the second.
What happens to the intensity, S, and direction of polarization of
unpolarized light upon passing trough three polarizers shown here?
E
S1 = S 0 / 2
E
E
and polarized
S 2 = S1 cos 2 25°
S 3 = S 2 cos 2 (70° − 25° )
S1
S2
S = S3
= S 2 cos 2 45°
S 3 = S 0 ⋅ 1 / 2 ⋅ cos 25° ⋅ cos 45° = 0.205 ⋅ S 0
2
2
Without the second polarizer
S 3 = S 0 ⋅ 1 / 2 ⋅ cos 2 70° = 0.058 ⋅ S 0
http://www.colorado.edu/physics/PhysicsInitiative/Physics2000/applets/lens.html
Electromagnetic Waves Produced by an Antenna
• When a charged particle
undergoes an acceleration, it
radiates energy
– If currents in an AC circuit
change rapidly, some energy is
lost in the form of EM waves
– EM waves are radiated by any
circuit carrying alternating
current
• An alternating voltage applied
to the wires of an antenna
forces the electric charge in the
antenna to oscillate
EM Waves by an Antenna
• Two rods are connected to an ac source, charges oscillate
between the rods (a)
• As oscillations continue, the rods become less charged, the
field near the charges decreases and the field produced
at t = 0 moves away from the rod (b)
• The charges and field reverse (c)
• The oscillations continue (d)
EM Waves by an Antenna
• Because the oscillating charges in the rod produce a current,
there is also a magnetic field generated
• As the current changes, the magnetic field spreads out from the
antenna
EM Waves by an Antenna
EM waves emitted by a simple vertical antenna are polarized.
The electric field is directed vertically.
The magnetic field is directed horizontally in circles around the
antenna.
The waves propagate horizontally, radially from the antenna.
Geometrical optics. Ray approximation.
Light is a kind of electromagnetic waves…
And waves are difficult!
In many cases, though, difficulties can be
avoided and geometrical optics can be
applied.
It is based on the suggestion that
Light travels in straight lines called
rays.
(Why do we suggest that btw?)
It is called ray approximation and it
reduces optics to ray tracing and
geometry. We do geometrical optics.
A ray a is a line in the direction along which light energy is flowing.
A laser beam (or a beam from your car’s headlight) is really a
bundle of many parallel rays.
Question: How come light waves can be reduced to
rays? Is it always valid?
Consider an unbounded plain wave of light.
All it takes to characterize it is its direction and intensity (which can be
thought of as density of rays). So, the ray approximation is OK.
After passing through an aperture the plain wave becomes a beam and gets
bounded. Does it keep going along a straight line?
Depends on the relation between the size of the aperture and wave length.
Ray approximation – waves on water surface
Waves propagate in straight lines
unless they hit something (a barrier
or an aperture) having a size
comparable with the wave length
In general all bounded light beams
in free space, including laser
beams, are somewhat expanding
and loosing their intensity (density
of rays).
They are expanding no matter how
hard you try to keep them narrow,
just because of the fact that they
are bounded!
What about spherical waves? Can we apply ray approximation to
them too?
Sure thing!
http://www.people.vcu.edu/~rgowdy/mod/104/sphraymv.htm#1
The ray model (continued)
Light travels through a transparent medium in straight lines called
rays, at speeds v = c/n, where n is the index of refraction of the
medium.
Light rays do not interact with each other.
A light ray continues forever unless it has an interaction with matter
that causes it to change directions or be absorbed.
• Light has four different ways in which it can interact with matter.
At an interface between two media, light can be reflected
or refracted.
Within a medium light can be scattered or absorbed.