When a wave moves, the individual particles that support the wave stay relatively in place. If the wave moves from left to right the particles may vibrate from left to right, or they may vibrate up and down. The WAVE MOVEMENT is the result of the orderly progression of vibration in the particles that make up the support medium.

For example, in a longitudinal wave, the particles vibrate in the same direction as the movement of the wave. The particles do not, however, go where the wave is going. They stay relatively in place.

On the other hand, in a transverse wave, the individual particles move perpendicular to the movement of the wave. They are still not going where the wave went. After the wave passes the particles that were affected by it return to where they started.

Sound is propagated as a longitudinal wave. The individual molecules of the air vibrate in the same direction as the movement of the sound. So, air molecules are necessary for sound to be heard. When the trees fell in the primeval forest they did indeed make a sound, even if no one heard them. Remove the atmosphere, however, and they will fall completely silently. Without air, sound is meaningless.

Light is propagated by transverse waves. But the 'medium' that supports the waves is not air, or 'ether' as was suggested by Huygens in the 1700th century. Light is propagated by electrical and magnetic disturbances.

There is an electrical resonance that vibrates in one direction, a magnetic resonance that vibrates perpendicular to the electrical resonance, and the wave is propagated perpendicular to both. Why is it hard for matter to travel at the speed of light? Because using this model, nothing is ACTUALLY travelling at that speed -- only the disturbance is travelling.

Remember, this is a MODEL. That means that we use concepts that we understand to try to understand more difficult concepts.

Look at the diagram of a wave on page 11. Waves have four properties, three of which interest us.

1. WAVELENGTH. This is defined as the distance from a particular point on one wave to the corresponding point on the next wave. It may be crest to crest, valley to valley, descending center point to descending center point, etc.


We have already talked about this a little bit: X-rays have shorter wavelength than visible waves, and visible waves have shorter wavelengths than radio waves. The more the energy in the electromagnetic wave, the shorter the wavelength. The less the energy in the electromagnetic wave, the longer the wavelength.

A meter is a little over 3 feet -- about 40 inches, in fact. Some waves in the radio portion of the spectrum have waves that are one meter from crest to crest. In the broadcast TV range, one wave may be 1,000 meters or even 10,000 meters long. A wave of yellow light, on the other hand, may be 550 nm long -- that means 550 x 10 meters long. Translation: 550. with the decimal point moved to the left 9 places (0.000,000,550 meters), or 550 divided by 1,000,000,000 (550/1,000,000,000 meters.)

Relatively small, in other words.

And X-rays have even shorter wavelengths.
 

2. Every wave in the electromagnetic spectrum travels at about 186,000 miles per second in a vacuum. Every wave. Radio, TV, X-ray, visible light, cosmic ray -- they all travel at EXACTLY the same rate in a vacuum!


When they enter the atmosphere they all slow down (the ones that are not absorbed) to different speeds. They are still fast -- but they are not all EXACTLY the same speed. As they enter another material, such as glass or water or diamond or body, they slow still further, depending on the density of the material and the particular wavelength. In glass, X-rays travel faster than blue waves, and blue waves travel faster than red waves, and they all travel faster than TV waves.

The longer the wavelength the more the wave slows in any given material except vacuum.

You may as well memorize that speed: 186,000 miles/second. Memorize a second speed: 3x10 meters/second. That is 3 with 8 zeros: 300,000,000 meters per second. We will use these two numbers frequently.
 

3. Imagine yourself expending the energy to swing a jump rope that is attached at one end. You might swing it once per second, or twice per second, or ten times per second or 100 times per second . . . The number of times you swing it is the frequency of the swings. I'll bet that if you were swinging it 100 times per second, and if it was a long rope, there would be more than one wave travelling along the rope in any given instant.


And your arm would be getting tired.

The higher the frequency, the shorter the wave will be, and the more energy it will take you to create the waves.

So now we will magically make the waves in the electromagnetic spectrum 'visible' to us, and stand still and count them as they go by. If they all travel at the same speed, there will not be as many of the waves that are one meter long going past in one second as there will be if they are 1/100 of a meter long. Right?
 

The shorter the wavelength, the higher the frequency, the greater the energy. The longer the wavelength, the lower the frequency, the lower the energy.

4. AMPLITUDE. This is the 'height' of the wave: the distance from the center line or 'average' to the crest of a wave or the valley of a wave. This is important in radio and TV. It is not one we will deal with in optics.

Second, the three attributes above that we are going to be interested in are related to each other. If we use v for the velocity (3x10 in a vacuum) and f for frequency and  for wavelength, then
     v = f

For example, in a vacuum, for a yellow wave with wavelength 560 nm,
     3x10 = (f) (560x10)

     v = f
              3x10
     f = -------------
            560x10

     f = 5.4x10 waves/second.

Hmm. OK, that means that for yellow light, 540,000,000,000,000 waves go by every second.

Well, OK, so you believe me just because you are required to, right? If you understood all of the last bit there, then read the part in the book called WAVE FORMULA on pages 13 and 14. If you don't even want to go back and reread what I just wrote, don't. I'm not going to expect you to do this. What I want you to know is that the three attributes, wavelength, speed and frequency, are related. The longer the wavelength, the lower the frequency. (And the lower the energy.) As the speed changes, one of the other two must change. What changes is the wavelength. The frequency stays the same for any given wave.

Not sure of that last statement?  We talk about visible light as a wavelength, as if that wavelength was inviolate.  In fact, the wavelength that we use for classification is the wavelength in a vacuum.  When the wave slows down, the wavelength changes.  Look back at the diagram for refraction and see that the distance between the waves decreased when the waves entered the slower medium, and increased again when the waves exited into the faster medium.  When the wave or ray changes speed the wavelength changes.  The frequency is what stays the same.

What I REALLY want you to remember is:

 

What the wavelength means. What the frequency means. What the speed is in a vacuum, in miles/second and in meters/second. How the three are related.      v = f  When the wave changes speed the wavelength changes.  The frequency stays the same. That the higher the energy, the shorter the wavelength, and the higher the frequency. That the lower the energy, the longer the wavelength and the lower the frequency. That cosmic rays and x-rays have the shortest wavelength, then UV, then visible light, next is IR, then microwave/radio/TV waves. That the greater the energy, the more the particle acts like a particle; and the lower the energy, the more the wave acts like a wave.

Finally for this week's lesson we are going to look at how rays help us understand what light does.

If you think of that light bulb giving off rays of light, then you can see that the rays will spread out from their source.

The definition of the word ray is the path that a particle takes. It is not a thing. It is a path. The photon is the thing. The ray is the slime trail that the snail leaves behind.

Going back to the idea that the rays spread out from their source, we have divergence. Two (or more) rays diverge if their photons are heading away from each other. You already know what divergence means, don't you?

Bet you think that you know what convergence means, too. It means that the photons are heading toward each other.

So we will just extend these two concepts, and talk about vergence. The vergence of two rays is their relationship to each other at one instant in time.

Look at the diagrams at the top of page 15. The rays that are diverging are travelling away from each other. We call this negative vergence. The rays that are heading toward each other are converging. They have positive vergence. Note that, once the rays actually pass each other, they start diverging. At the point where they meet they have zero vergence.

When two rays that start out travelling incredibly close to each other travel a long distance from where they crossed they will begin to look parallel to each other. The rays have to be an infinite distance from the source to actually be parallel. We say that if the rays are 20 feet or 6 meters from the source then they are parallel to each other; this is, again, optical infinity.

Finally, look at the diagrams at the bottom of page 15 and the top of page 16. We have already discussed the ray, which is a single path of a single photon. Many people like to say that the ray is the path of the smallest particle that would be able to go through an extremely small hole in each of two screens.

A beam is a group of pencils.  It can be all of the pencils that are emitted from the source.

And that is all for this module!

Do the work sheet from the link on the assignment page, and submit it to your instructor.  That is how you will receive credit for attending class for this module, and it will help your instructor see if you understood the material.

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