# Light wave theory

1. Dec 11, 2003

### matrix_204

Could anyone please explain me the concept of light waves and the information about polarization. Also the inferometers or some stuff on nodal lines, these sections are really confusing me about the whole thing. I dont have a clear picture of what its all about.

2. Dec 12, 2003

### turin

Light waves, depending on the context, usually refer to electromagnetic waves in the region of the spectrum around the visible frequencies/wavelengths. This includes the colors you see (visible region), and usually also considers down to the far infrared and up to the far ultraviolet. Millimeter waves, the next region down from infrared, are usually considered as radiowaves as opposed to light waves. X-rays, the next region up from ultraviolet, are usually considered as high energy radiation, as opposed to light waves. They are all electromagnetic, though, and the naming convention is secondary to the physics.

As electromagnetic waves, some generalities can be made. There are two fields involved, the electric and the magnetic. (Really these are just two ways in which the same fundamental field manifests. This is probably beyond the scope of what you are trying to understand.) The electric and magnetic field vectors are perpendicular to each other in the wave. They are both also perpendicular to the direction of the wave, and so the wave is called "transverse." The polarization is defined by the direction of the electric field vector. (You will probably only be dealing with linear polarization. For this, the polarization does not change direction.)

For the wave traveling in the z direction, the electric and magnetic fields oscillate in the x-y plane. Let's say that the x-direction is horizontal, and the y-direction is vertical. If the electric field oscialates in the x-direction, then the wave is horizontally polarized. If the electric field oscillates in the y-direction, then the wave is vertically polarized. If the electric field oscillates in some direction that makes some angle, &theta;, with respect to the x(or y)-axis, then the wave has a polarization angle of &theta; with respect to the x(or y)-axis.

I'm assuming you meant to write "interferometers." An interferometer is, generally, an piece of equipment designed for the purpose of causing interference. General waves can be thought of as composed of more fundamental constituents, called plane waves. A plane wave is a sinusoidal variation in space and time. In general, waves are not sinusoidal. We break them up into sinusoidal consituents because sinusoids are easier to manipulate in calculations. You will probably only be considering plane waves, so this decomposition is somewhat trivial, but it gives insight into how interference works.

In a way, waves exist everywhere in the region of interest. The wave is the value of the thing that is waving at every point in space and time. So, you can think of two light beams as two distinct light waves, or you can think of this situation as one wave that is the sum of the two individual beams. Where one beam is zero, the total wave is just trivially the other beam. But, in the region of space where both beams meet, the total wave is a nontrivial sum of the two. Mathematically it is a sum. Physically it is interference. It is straightforward. If the E-field of one of the beams is in the same direction at a point as the E-field from the other beam, there is constructive interference. The total E-field is the sum of the two individual E-fields. If the individual E-fields are the same size but pointing in opposite directions at some point in space, there is destructive interference, and the total E-field, being the sum of the individual E-fields, is naturally zero. This is called the principle of superposition.

Since the waves are functions of space and time, in general these points of constructive and destructive interference will move around. If the light is coherent, then it is possible to establish stable, nonmoving patterns. Usually, interferometers have a viewing screen, which is just choosing a region of space to observe the interference. The interference happens everywhere where the two beams exist in the same space, but you usually are only interested in what is happening on the screen.

I don't know what is meant by nodal line, but, I would assume, if this is in the context of an interferometer, that this refers to the dark lines that appear on the screen of the interferometer. They appear dark because on these lines there is destructive interference of two (at least) beams of light. I should mention that the light can be from the same source. A beam splitter can be used to separate the light into two beams so that the light from this common source can be made to interfer with itself.

Last edited: Dec 12, 2003
3. Dec 13, 2003

### matrix_204

hey thnx alot of your information, it was really helpful, since i had not idea at first what the concept of light waves was, but now i can at least have a picture of it. I was wondering, there are some formulas used in light wave theory, and when solving those problems its mostly seems to be just plugging in the numbers and thats it, so my question is whether this is ok when solving problems. just to get an idea.

4. Dec 13, 2003

### dlgoff

There are lots of areas from optics alone to boggle the mind. However there are some optical design programs/software where you can plug in parameters in designing systems.

5. Dec 15, 2003

### matrix_204

can you give me a small idea on particle theory, and wave theory.

6. Dec 15, 2003

### turin

This is strictly my own oppinion, but there is two years of engineering experience behind it. When solving a problem, it will always come down to plugging something into something, and seeing what comes out. Of course, you will want to know at least where your formula came from, and in what ranges it is applicable, but, assuming that you can take these issues as trivial, then all it boils down to is plugging numbers into your formula and considering the result. If you are using a computer, then there will be other considerations, because computers (and that includes calculators, so this includes really any type of problem you would solve) solve strictly numerically (as far as I have heard). You would have to worry about dividing by a very small number, for instance, because the computer usually rounds sufficiently small numbers to zero. (I have even run into a divide-by-zero problem on a calculator)

Sort of an opposite question could be, "Is is OK to solve problems without plugging numbers into a formula?" I can't think of any problem you could try to solve that you could neglect plugging some kind of numbers into some kind of formula, so I would say that, not only is it OK to solve problems in the way you're asking, but it is absolutely necessary to do so. Again, I will emphasise that this is not based on experience in physics, but in engineering.

Last edited: Dec 15, 2003
7. Dec 15, 2003

### turin

From my understanding:

Waves must be defined over all space (all space where a non-trivial consideration is being made). There are usually ways to break the definition up into components/constituents, to simplify things, i.e. breaking the description up into a set of basis functions like sinusoids, or the ray theory of optics which is a dual theory to the wave theory if I understand it correctly.

Particles are defined to strictly exist at one singular point in space. They are either fermions or bosons. Fermions are the "hard particle" type particles (or, I should really say, "the notion of a fermion is the closest notion to "hard particle" that survives in modern particle theory"). Bosons are particles in the sense that, if you want to "inquire" of the boson where it is in space (measure its position), then it will "tell you" that it is at a particular point in space (its wave function will collapse to a position eigenstate). A boson is quite a bit different from the old "hard particle" notion in that a bunch of bosons can be at the same place at the same time (they don't "feel crowded").

The electron is probably the most commonly used fermion for examples.

The photon is probably the most commonly used boson for examples.

Last edited: Dec 15, 2003