Physics 202
Intro to Astronomy:  Lecture #5
Prof. Dale E. Gary


Light in Everyday Life

When we go outside on a sunny day, we see the light from the Sun reflecting everywhere, and at the same time, we feel the heat from the Sun.  Both light and heat are forms of radiation.  Nearly everything you see outside on a sunny day is due to reflected light from the Sun.  Imagine removing the sunlight (or wait until nighttime), and everything will be black and invisible.  Then you will see only things that have their own source of light, or perhaps objects that reflect that light.  So most of what we see is from reflected light.

Light can react with matter in four ways:

Note that most objects will do several of these things at once.  A piece of glass will both transmit and reflect light.  It will also do a little absorption, especially if it has some coloring.  We say that a piece of red glass is transparent, but partially opaque to other colors.  A red piece of non-transparent plastic will be mostly opaque, but may allow a little light through.  All of the variety of colors and surface textures we see outside on a sunny day are entirely due to the interaction of sunlight on the objects we see--a green leaf, a rainbow from a sprinkler, a fuzzy caterpillar, our face reflected from the side of an automobile.  We can understand it all, at least on a basic level, by considering the above four interactions of light with matter.

Consider the light from the light bulbs in this room.  Some of it goes directly out the window, but most of it reflects off from the various surfaces. The content of this reflected light changes, taking on information about the surface it reflected from.  Your eyes and brain are well adapted to receive this reflected light and interpret it, without your having to be concious of it at all.  However, your eyes still do not receive all of the information available.  For instance, your eyes are only sensitive to light waves in the visible.  With infrared goggles, you will see other information--objects actually glow on their own due to their heat, giving off light at (infrared) wavelengths your eyes are not sensitive to.  The sunlight contains ultraviolet light that your eyes cannot see, yet that is what gives you a sunburn.

Properties of Light
When we pass light through a prism, or past a diffraction grating (e.g. the grooves in a CD), it is broken up into colors.  The colors are merely the interpretation your brain gives to the different wavelengths of the light.  To understand light, you have to understand the properties of waves.  Yet light (just like every other form of matter) can be thought of as both particles and waves at the same time (wave-particle duality).  The smaller something is, the more apparent its wave-like properties, and the larger (more massive) something is, the more apparent its particle properties.  Light is the ultimate light particle--it has no mass!--so it shows very strong wave-like properties.  We call it an electromagnetic wave.  Still, it also has particle-like properties, and we call the particles photons.

The properties of waves are:

You might guess, just from the units, that wavelength and frequency are related to speed.  In fact, the product of the two, wavelength times frequency equals the speed.  Because the wave speed is constant, that means that longer waves must have a lower frequency. In the case of light, the wave speed is the speed of light, c = 3 x 108 m/s.
The Many Forms of Light

We already have been talking about several forms of light--visible light, infrared, ultraviolet.  In fact, there are several more, and they are all exactly the same phenomenon--an electromagnetic wave--and they all have the same speed (the speed of light)--but they differ in wavelength (or equivalently, in frequency).  Electromagnetic waves are different from other waves in one important way: they do not need anything to "wave" in! They can travel in a vacuum. Sound waves, for example, cannot--they have to have something to travel through.

Here is an overview of the forms of light:

Notice how wavelength increases in one direction and frequency increases in the other direction, so that the product of the two is constant, and equals the speed of light.

We said earlier that less massive things display wave-like properties, but it is more accurate to say less energetic things display wave-like properties.  As it happens, photons with higher frequency also have higher energy.  So photons at the long-wavelength (low energy) end of the spectrum (e.g. radio or infrared) behave mostly like waves, but at the short-wavelength (high energy) end of the spectrum (X rays and gamma rays) behave more like particles.  The high energy of X rays explains why they can pass through solid objects like people, so that you can see your bones and internal organs in an X ray photograph.

You should memorize the wavelength, frequency and energy order of these forms of light, e.g.

Note that the order for energy and frequency is the same.

This is called the electromagnetic spectrum.  A spectrum generally is the splitting of light into its colors, but our eyes can see only visible light colors (red through violet).  Visible light is only a small part of the entire spectrum.  The other terms, like infrared, or ultraviolet, can also be referred to as colors of light, even though they may be invisible colors (to our eyes).  We have to develop techniques to detect these invisible colors (e.g. radio antennas can pick up radio waves, IR goggles can detect infrared, photographic film can detect X-rays, etc.)

Lecture Question #1

Light and Matter

When we raise the temperature of a body, it first glows only in the infrared, being dark to our eyes. But when hot enough it starts glowing a dull red that we can see, then bright red, then yellow, then blue. 

We can see this effect in a flame, where the flame is blue at the bottom, where it is hot, but it cools as it rises and becomes white-yellow, then red where it is coolest.

If we take such a body and spread out its light into a spectrum, what would we see?  We would see a smooth rainbow of colors, but the brightest part of the rainbow would shift to higher frequencies (bluer colors) as we raise the temperature.  This smoothly varying spectrum is called a continuum spectrum because it is made up of all possible frequencies.

Above is a plot of continuum spectra for different temperatures.  You can see the narrow part of the overall spectrum that corresponds to what our eyes can detect.  The spectrum for a human body is far to the right (longer wavelengths) of what our eyes can see. That is why we cannot see humans glowing. 

Unless, of course, we have an infrared camera. Notice that these people are glowing, except the person on the left has cool fingers!

A 3,000 K object (like a star), can be seen to glow with much more red light than blue light, so it looks red.  The Sun, at 6,000 K, peaks exactly in the middle of the visible, so we see all colors equally (so the sunlight looks white).  An even hotter star, at 15,000 K, will appear blue, but its real peak is in the ultraviolet where we cannot see. There is a quantitative relationship between wavelength of light and temperature, called Wein's Law. The relationship is wavelength proportional to 1 / temperature (lambda ~1/T). So if you double the temperature of something, you halve the wavelength.

Such continuum spectra are what we see from objects that are in equilibrium at some temperature.  From the spectrum we can determine the temperature, so we have no problem telling the temperature of stars.  But the light contains MUCH more information than this.  For example, consider a green leaf.  The leaf is green because it absorbs all colors of light except green.  The green light is reflected, and that is why we see the leaf's color as green.  Consider the sky.  It appears blue because the air reflects (or a better term is scatters) the blue light, letting the other colors, especially red, pass through.  We say it is transparent to red, but only partially transparent to blue.  Of course, air is clear, so it is very transparent to all colors, but if you see the setting Sun through a lot of air, you can see that the Sun becomes red.  That is because almost all of the blue light doesn't make it to our eyes--it is all scattered away.

Not just air, but any gas is good at absorbing (or scattering) some colors and good at transmitting others.  In fact, if you heat a gas it emits the same colors that it absorbs.  If you split the colors of a glowing gas, such as a candle flame or a neon sign, with a prism or diffraction grating, you will see that it emits only in certain narrow bands of color.  These bands are called spectral lines.  Here are some characteristics of spectral lines:

Spectral Lines and the Blackbody Spectrum

The spectral line intensities are related to the temperature of the body doing the emitting.  In the case of the
5000 K gas in front of the 6000 K background, the background has a normal Planck Function blackbody
spectrum except where the cooler gas is absorbing it.  The depth of the lines reflect the 5000 K blackbody
spectrum of the gas.  In the case of the 5000 K gas with a cool background, the height or intensity of the
spectral lines reflects the 5000 K blackbody curve of the gas, but only in the spectal lines.  At other wavelengths,
the gas has no emission, and so is dark.

Select the Light and Spectroscopy tutorial on Astronomy Place web site and go through it.

Lecture Question #2

Spectral Lines and the Doppler Shift

When you hear a car or train go by, you will hear the pitch of the sound go from a high pitch to a low pitch. That is because the car or train is going a good fraction of the speed of sound, and the waves "bunch-up" ahead of the vehicle and "spread-out" behind it. The pitch, or frequency of the waves get higher ahead and lower behind, and that is what we are hearing. This effect is called the Doppler effect. By measuring the amount of shift in the pitch, we can measure the speed of the vehicle.

The same thing happens for light, but notice that the speed of the object has to be high enough compared to the speed of light, which means the object has to be moving fast indeed. In this case, it is not a "pitch" change that we hear, but a color change that we see.

Fortunately, we can use markers in the spectrum of light--the spectral lines--to make very accurate measurements of shifts of spectral lines. From these shifts, we can detect even rather small velocity changes.

Select the Doppler Effect tutorial on Astronomy Place web site and go through it.

Lecture Question #3

When you are finished with these tutorials, you should know that from starlight we can determine

We can also put this information together to determine other things.  If we see star's spectral lines shifting back and forth we can guess that an object (another star or a planet) is orbiting it and causing the star to move in a circular path.  From the period of the shifts, we can tell the orbital period of the object.  If we know the mass of the star, we can determine how far the object is from the star.  Or if we know how far the object is away, we can determine the mass of the star.