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1. Wave Optics
The light is a form of electromagnetic
wave (radiation). But, how do we know?
Basic features of the light wave:
Interference
Diffraction
Polarization

2. What Is A Wave?
There are many examples of waves in daily life:
Water wave, sound wave, human wave in a
stadium, …, but what is a wave?

A wave is a A wave is a propagating disturbancepropagating disturbance of some of some
equilibrium, quiescent state.equilibrium, quiescent state.
A wave needs a medium, like air, water, people in a
stadium. The medium consists of individual “particles”
which are normally in a “motionless”, equilibrium state.

3. Disturbance?
Parts of the medium or some “particles” in the
medium move away from the equilibrium because
of an external force acting on it.
In many examples, the motion of the
“particles” is simple harmonic.
Particles in the medium is interactive, when
one is off equilibrium, it drags it neighbors
into harmonic motion as well (with a little time
delay:). Then the disturbance of one particle
can propagate in the medium => Wave!Wave!

4. Superposition of Two Waves
When two waves come together, what
happens?
The displacement (or disturbances) will add
together (SUPERPOSITION)
If at a point in the medium, two waves are
pulling in the same direction, the displacement
will be the sum of the two individual
displacements.
If two waves are pulling in the opposite
directions, the resulting displacement is the
difference.

5. Phase Relation
The result of the superposition of two waves
depends not only on the magnitude of the
waves, but also on the phase relation.

When the waves are in phase, the two crests
coincide, they reinforce each other, the net
result is a large net motion.

When the two waves are out of phase, the
crest of one wave meets the valley of another,
the net result is a cancellation.

6. Example of adding waves

7. Interference
When two arbitrary waves are superimposed, the
result is very complicated….
If two waves have the same wavelength,
the locations of reinforcement and
cancellation may be fixed in space for a
long time, making in possible to SEE the
superposition. We call this phenomenon
“Interference”
There are then destructive and
constructive interferences.

8. Sine wave and its properties
When the particle’s motion is harmonic,
the medium can support the simplest
wave: Sine Wave.

FrequencyFrequency of a Sine Wave = frequency
of every particle’s oscillation frequency.
Wave lengthWave length  the distance from the
nearest particle which does the same
oscillation.

9. Example I: Interference
from two point sources.
Constructive source at nearly the same
place (figure)
Destructive source at nearly the same
place (figure)
Small unmounted speakers
Two sources separated by half a
wavelength.
Same phase.
Out of phase.

10. Two sources at the same place..

11. Two sources half-wave length apart

12. Coherent light
If the light is a wave, how come that we
don’t see much of the interference
phenomena?
We need two sources of light with FIXED
phase relation. If the phase is not fixed and it
jumps around, the interference gets washed
out. Most of the light sources have very short
memory of phase and are incoherent.
If two light sources have a fixed phase
relation, we call then Coherent.

13. Thin Film Interference I
When the light is reflected from a thin
films, there are two reflections: from the
front surface and the back one. The two
reflections have a fixed phase relation
and interfere coherently.
In the first case, the reflection is hard and
there is a 180 degrees of phase difference.
The second reflection is soft, yielding no
phase difference.

14. Two coherent wave from reflection

15. Thin Film Interference II
If d is the thickness of the film, 2d is the
extra distance the second reflection
travels. If 2d is ½ of the wavelength, the
two reflections interfere constructively:
very little transmission.
If 2d is equal to integer number of
wavelength, two waves interfere
destructively: 100% transmission.

16. 2d is the half-integer wavelength

17. 2d equals to the integer number of
wave-length

18. Thin Film Interference III
The thickness of a film may vary, from
which we can find interference patterns
Applications:
Camera lens coated with a thin film to
reduce the reflection.
Can only do for one wavelength.
Question: what do you see when there is
a layer of oil on the surface of water?