# More on Light and matter

### Blackbodies

A blackbody is something that exists only in a mathematical model - it is not possible to make a real one, although we can get close. If you had a blackbody in your hand, it would look blacker than anything you have ever seen. It would absorb ALL energy that falls on it. Take the blackest thing you can find and shine a bright flashlight on it. If you see a spot of light on the object, it is reflecting some of the light. A true blackbody would not reflect ANYTHING, so the flashlight beam would not be visible.

When heated above absolute zero, a blackbody emits energy in a precise pattern known as the Planck curve. This is illustrated on p. 53. The temperature of the warm/hot object determines the Planck curve of emission. By the way, this curve is also known as the blackbody curve.

Another thing - a blackbody can be taking energy by absorbing radiation and also emitting radiation according to Stefan's Law. If the energy coming in exceeds the energy being radiated out, the blackbody will be warming up. If the energy coming in is less than what is going out, the object is cooling. If the incoming and emitted energies are equal (in balance), the object is in radiative equilibrium. Its temperature will be stable.

The Earth is in radiative equilibrium. It takes in energy from the Sun on its daylight side and radiates infrared all around. The equilibrium temperature is 255 K, or about 0 degrees Fahrenheit. That's COLD! Ask Google for "earth equilibrium temperature" and you will get some good examples.

### Spectroscopy

Spectroscopy is, quite simply, spreading light out by wavelength so you can study each wavelength in detail. Your book shows this being done by a prism; modern astronomers do it with a diffraction grating, which does the same thing but is more efficient.

Spectroscopy is the heart of astronomy now. Analyzing the spectrum of light from a distant object reveals a lot about the object. There are three types of spectrum for us to look at.

• 1. Continuous, or rainbow. Home of ROYGBIV.
• 2. Emission line spectrum. Bright lines on dark background.
• 3. Absorption line spectrum. Dark lines in continuous spectrum.

Here's a nice illustration.

Let's see how that works. Suppose you use your handy-dandy spectrograph to look at the light from some distant object. You measure carefully and find that the light follows a blackbody curve, which means that you see a rainbow (ROYGBIV). What can you know about the object??

First - you know that the object is emitting radiation like a blackbody, which means that it is a solid or very dense gas. You can also use Wien's Law to find out its temperature since you have measured and found where the peak is.

Here are a couple of links to good interactives demos of Planck curves.

Now for bright lines; here we have an emission spectrum. The light consists of bright lines of pure color separated by darkness. Definitely not ROYGBIV! This kind of light is emitted by a low-density gas.

Emission spectrum examples:

Finally we get to absorption lines. The mechanism that produces an absorption spectrum is a bit more complex. Here we have light from some incandescent source (continuous spectrum) passing through a low-density gas. The gas atoms have the property of absorbing light at the same wavelengths they will emit. This produces gray or dark lines across the continuous spectrum.

To illustrate this, we can use a really goofy story.

imagine a football field. On one side of the field is a guy with a large bin of tennis balls, having equal numbers of red, yellow, green and blue tennis balls. On the opposite side of the field is another guy with four boxes, labelled "red", "yellow", "green" and "blue." To start off, the guy with the bozes of tennis balls will pour all 4 boxes together in a large bin and mix them up thoroughly. These will form the "light" of our thought experiment. On the opposite side of the field we have another guy with four empty boxes, one marked red, one marked green, etc. One for each color of tennis balls. In the middle of the field we have a goofball with a net. More on him in a minute.

The experiment goes like this: the guy with the huge bin of mixed color tennis balls begins grabbing balls from the bin and throwing them across the field to the guy on the other side. This other guy catches the balls and puts them into the appropriate boxes, sorting them by color. When all of the balls have been thrown across, the receiving guy will have 4 boxes of colored tennis balls, sorted by color. The thrower corresponds to a white (or close) light source emitting light and the catcher is an astronomer with a spectrograph, sorting the light by color.

Now repeat the experiment, except that this time the goofball in the middle gets into the act. He has a fetish for red tennis balls (he's really weird). As each tennis ball comes over, he looks at it. If it is not red, he lets it go by. If it IS red, he tries to get it with his net. He doesn't get all of the red ones, but he does get some. Now for the really goofy part - after he gets one, he looks at it, grins, and throws it out in any random direction. Doesn't keep it - just looks at it and tosses it away. This goes on till all the balls are thrown as before.

At the end, what do we have? The catcher has 4 boxes of tennis balls, sorted by color, just like before except that there is a shortage of red balls. The goofball in the middle got some. Those red balls are scattered all over the field. The catcher can tell by the shortage of red balls that there is something that is absorbing red tennis balls.

Now imagine that you are an observer that can move around and view the scene from any direction. If you join the catcher on the side of the field, you see tennis balls of all colors (white light). If you go out onto the field and look at the weirdo with the net, the only balls you see coming at you will be red; the other ones are passing overhead.

In this second experiment, the catcher and thrower are as before. The weirdo in the middle corresponds to a cloud of gas between the light source and the astronomer. The gas is absorbing photons at specific wavelengths (colors) determined by the structure of the atom. The energy absorbed is reradiated in random directions. This is an emission line spectrum. The catcher sees a shortage of red balls - this is an absorption spectrum.

Be sure to read the book about the spectrum of hydrogen, radiation as a particle and more complex spectra.

### Doppler Effect

Doppler effect is an effect of motion. Doppler effect is simple. It is caused by motion.

The formula on page 65 is one form of the relation. Here's another

((apparent - true) / true) X c = velocity.
Here "apparent" means observed wavelength, "true" means actual wavelength, "c" is the speed of light (this is normal notation for it), and "v" is the velocity of the object toward or away from you. This form is useful because the sign of the term
(apparent - true)
tells you something. If this difference is positive (apparent greater than true), the object is receding (moving away). If the difference is negative, the object is approaching.

Here is an excellent Doppler effect example. Here's an explanation of the effect. Look at the figure on the left and count the frequency of waves passing that observer. Then, as the observer starts to move, keep counting the frequency. You'll see the frequency increase as the observer moves toward the source, then decrease as the observer moves away from the source. Note that the same effect occurs if the source is moving and the observer is not.

Be sure to use the end-of-chapter reviews.

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