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

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 propagating disturbance of some equilibrium, quiescent state. A wave is a propagating disturbance of some 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.

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. Wave! 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!

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.

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.

Example of adding waves

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.

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

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.

Two sources at the same place..

Two sources half-wave length apart

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.

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.

Two coherent wave from reflection

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.

2d is the half-integer wavelength

2d equals to the integer number of wave-length

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?