Understanding Waves

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Understanding Waves

Before going any further, it's important to understand light waves. Look at Figure 1.2 for an example.

Figure 1.2. Waves have an amplitude (or height) and a wavelength.

graphic/01fig02.gif


Almost all objects in nature proceed with a twisting or turning motion in time, called vibration . When sound is released from a speaker, the vibrations continue for some time before they fade outthis changing motion in time and space creates a wave . A wave cannot be still because it exists only in movement from one point to another.

Take a look at the sine wave in Figure 1.2. The distance from one ascending part of the wave to the next is the wavelength . Just think of each maximum point being repeated in the next wave, and measure the distance between them. The sine wave for light is repeated billions of times a meter (hence visible light's wavelength is measured in nanometers), whereas water waves are measured in centimeters or meters based on the water's area.

The number of times each vibration occurs per second is the frequency . Figure 1.2 shows a midline running straight through the sine wave from left to right. The measurement of distance from the midline to the peak of the wave (also known as the crest ) is called the amplitude . The speed of a wave is equal to its wavelength times its frequency. Another important point to understand is that each vibration per second is called a hertz .

Consider the following equations:

 Frequency = 1 / Period; Wave_Speed = Frequency * Wave_Length; 

A 60-hertz wave, therefore, vibrates at 60 times a second and has a period of 1/60 of a second.

It's hard to visualize electrical waves because we can't see them with the naked eye. If you run a bamboo stick back and forth through still water, you'll create waves on the water's surface. Electromagnetic waves can be visualized in the same manner as the ripples.

Electromagnetic waves are created by an electrical current as well as a magnetic field. An electrical current can come from a power source such as a battery. Electrical current can produce the magnetic field.

Let's say you connect a rod to a power source with a high current. What happens? The rod becomes electrically charged. Now if you go into an open room and shake the rod around, it will produce electromagnetic waves in space. This creates an electrical current, which is overlaid with a magnetic field. The magnetic field is produced by the force of the moving electrical charge. Because you're shaking the rod, it's a changing electrical current with a changing magnetic field. Figure 1.3 shows an electromagnetic wave.

Figure 1.3. An electromagnetic wave is made up of an electrical current,overlaid with a magnetic field.The magnetic field is produced by the force of the moving electrical charge.The two fields are perpen dicular.

graphic/01fig03.gif


These two fields are perpendicular to each other, but travel in the same direction, thus the total wave is described as being transverse and travels through space in a linear motion at one constant velocity, the speed of light C.

Electromagnetic Wave Velocity

You may be saying to yourself, "This is great to know, but why do these waves travel at one constant speed?" Should you believe it just because I said so? Well, let's think about it for a moment with the help of Albert Einstein. Einstein said that no mass can accelerate to the speed of light; he never said something can't travel faster than light if it's already going faster! However, he did say that nothing with mass can be accelerated to light speedperiod. The equations that govern this rule say that the amount of energy you would need to accelerate an object to light speed is infinite. Thus, nothing with mass can travel at light speed, but objects without mass travel at exactly light speedthis is what light ispure energyso it doesn't break the rule.

Visualize a light wave moving in space, traveling to infinity with no loss of speed. Now, it is possible to change the frequency of light, which will in turn cause the color of the light to change.

I still haven't explained why light moves at a constant speed. Let's say you're able to slow a light wave down. This causes weaker electrical and magnetic fields. As the wave moves through space, the fields become weaker and weaker until the wave fades out. Is this possible? Well, not according to the laws of energy conservation and electromagnetic induction, which say energy can't just disappear. Remember, energy can never disappear; it can only change form.

Or let's say you speed up the light wave. This creates stronger electrical and magnetic fields, which causes the wave magnitude to increase exponentially in energy. This is also illegal according to the laws of energy conservation. Energy must flow at one constant speed to keep it in an equal balance.

James Maxwell calculated the speed of this wave at around 300,000 kilometers per second. Maxwell also found out that visible light was just radiation within a fixed segment of the electromagnetic spectrum. Visible light's range is measured from 4.3x10 14 to 7x10 14 vibrations per second. Our eyes are only equipped to see waves within this range, that's why it's called visible light!

If you look in Extras/Chapter1/ on the CD there is a Java example of the electromagnetic wave. You can actually see a demonstration of the electromagnetic wave in action by opening Propagation of Electromagnetic Wave.htm in your favorite Web browser. I found this page at http://www.phy.ntnu.edu.tw/.

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Focus On Photon Mapping
Focus On Photon Mapping (Premier Press Game Development)
ISBN: 1592000088
EAN: 2147483647
Year: 2005
Pages: 128
Authors: Marlon John

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