# Light and Matter

The nature of light emitted by an object will give you clues about the nature of the object that emitted the light.

That's the heart of the story. Astronomers study light in order to find out about things in the universe, partly because it works and partly because light is the only thing available to study! Biologists can study specimens in the laboratory, chemists can study chemical reactions, but astronomers have to make do with light.

We start with waves. A wave is a disturbance propagating through something. Figure 2.2 shows a wave in water. The wave is a disturbance, not a flow. If you watch something floating on the water, you will notice that it only moves up and down; it does not move outward with the wave. The wave is carrying some energy - it takes energy to lift the water. A mechanical device with a float on the water surface could extract a bit of useful energy from the wave. This animation shows an electromagnetic wave as two components: electric and magnetic fields at right angles to each other. In the case of sound, a medium (solid, liquid, gas) is required. There is no sound in vacuum. By the way, the speed of sound at sea level is roughly 1,100 feet per second or 340 meters per second. It varies with altitude. Electromagnetic radiation consists of changing electric and magnetic fields propagating together at the speed of light. No medium is required - electromagnetic radiation travels perfectly well in vacuum.

We are presented with three properties of a wave: amplitude, wavelength, and velocity. Amplitude is simply the height, or intensity, of the wave and is independent of velocity and wavelength. There is a fourth property, namely frequency, which is the number of waves passing by your detector every second. Frequency can be calculated from wavelength and velocity. Wavelength, velocity, and frequency are related.

wavelength X frequency = velocity

That's an easy relation.

And now for something only slightly different. You are all aware that you are able to determine the direction a sound (like a voice) is coming from with your eyes closed. Your ears and brain do the job. How does this work? What is your brain doing that lets you do this?

First - your ears are something like 6 inches apart (more if you have a big head!). The wavelength of human speech is something in the area of 2 feet. This means that your ear spacing is on the order of 1/4 wavelength. If the sound is coming from the side, your ears are separated by 1/4 wave, which means that if one ear is hearing the peak, the other is hearing the zero crossing. Your brain is capable of combining this with the relative loudness in both ears and determining the direction to the sound. If your brain detects equal phase and loudness, the sound is directly ahead.

If your ear spacing is either a very small fraction of a wavelength (very low frequency) or much larger than a wavelength (very high frequency), you will not be able to localize the sound. Consider the fact that an audio system's subwoofer (very low frequencies) can be placed ANYWHERE in the room. You are not able to tell where those low frequencies are coming from.

End of digression.

Radio waves, light, infrared, and other ranges of electromagnetic radiation travel at the speed of light. That speed is usually written in one of three ways.

300,000,000 (3 x 108) meters per second
300,000 (3 x 105) kilometers per second
186,300 miles per second

Use the one appropriate for calculation at hand.

Now for a brief summary of the units we'll use. You all know that a meter is 39.4 inches. A centimeter is 1/100 of a meter. A millimeter is 1/1000 meter. A micrometer (or micron) is 1/1,000,000 million (10-6) of a meter. Finally, a nanometer is one billionth of a meter (10-9). We will use nanometers (nm) to measure the wavelength of light. A nanometer is VERY tiny, but it makes the numbers reasonable (400 to 750).

Visible light ranges from about 400 nm to just over 700 nm. You perceive the difference in wavelength as color. 700 nm light is very red while 400 nm light is very violet. If you mix light of all wavelengths in the range at equal amplitude, your eye will perceive white light.

Remember ROYGBIV? That's all colors in the visible spectrum (a rainbow). Figure 2.7 shows the colors but leaves out indigo. Without indigo you get ROYGBV, which isn't quite so good.