Tuesday Mar. 4, 2008

A new Optional Assignment was handed out in class today.  The assignment is due at the start of class next Tuesday, Mar. 11.

The Experiment #2 reports and the revised Expt. #1 reports were collected in class today.

The Experiment #3 materials will be distributed this week.

How to safely jump start a car with a dead battery.
We'll spend at least the next two class periods on electromagnetic radiation.  It is the most important energy transport process because it can travel through empty space. 

To really understand EM radiation you need to understand electric fields.  To understand electric fields we need to quickly review a basic rule concerning static electricity.

The rule is illustrated above.  You'll find this summarized on p. 59 in the photocopied Classnotes.
Now imagine, as shown below, placing a + charge at three different positions (a, b, & c) around another center charge.

Each of the charges is going to be repelled by the center pushed.  The charge at (a) will be pushed to the left with a fairly strong force (because it is closest to the center charge).  The charge at (c) is further from the center and will be pushed to the upper right with a weak force.  Charge (b) will pushed to the right with medium strength force.  These various forces are shown on the next figure.

With just a little thought you can see that if you were to place + charges at other positions you would eventually end up with a pattern like shown at the bottom of p. 59 in the photocopied Classnotes.

This is the pattern of the electric field vectors or arrows around a center + charge.  The arrows tell you the direction and strength of the force that would be exerted on a second + charge placed anywhere is the figure.  We will use these electric field arrows to understand the behavior of electromagnetic radiation.
The figure on p. 60 has been split into 3 pieces and redrawn below for clarity.

We imagine turning on a source of EM radiation and then a short time later we take a snapshot.  During this time the EM radiation has propagated off to the right.  If you could see the radiation you would see a wavy pattern of electric and magnetic field arrows.  We'll ignore the magnetic field lines.  The E field lines sometimes point up, sometimes down.  The pattern of electric field arrows repeats itself. 

Note the + charge near the right side of the picture.  At the time this picture was taken the electric field arrow at the position of the + charge indicates that the radiation is exerting a strong upward force on the charge.

Textbooks often represent EM radiation with a wavy line like shown above.  The first snapshot figure above shows us what this wavy line really represents.

The wavy line just connects the tips of a bunch of electric field arrows.
Now we take another snapshot a short time later.  The wavy pattern has moved to the right.

The EM radiation now exerts a relatively weak downward force on the + charge.

And finally one more snapshot.

The + charge is now being pushed upward again.  A movie of the + charge, rather than just a series of snapshots, would show the charge bobbing up and down much like a swimmer in the ocean would do as waves passed by.

The wavy pattern used to depict EM radiation can be described spatially in terms of its wavelength, the distance between identical points on the pattern.  By spatially we mean you look at different parts of the radiation at one particular time.

Or you can describe the radiation temporally using the frequency of oscillation (number of up and down cycles completed by an oscillating charge per second).  By temporally we mean you at one particular point for a period of time.
One way of producing EM radiation is to move an electrical charge up and down.



 You add energy when you cause an electrical charge to move up and down and create the EM radiation (top).
In the middle figure, the EM radiation then travels out to the right (it could be through empty space or through something like the atmosphere). 

Once the EM radiation encounters an electrical charge at another location (bottom right), the energy reappears as the radiation causes the charge to move.  Energy has been transported from left to right.
EM radiation is created when you cause a charge to move up and down. If you move a charge up and down slowly (upper left in the figure above) you would produce long wavelength radiation that would propagate out to the right at the speed of light.  If you move the charge up and down more rapidly you produce short wavelength radiation that propagates at the same speed.

Once the EM radiation encounters the charges at the right side of the figure above the EM radiation causes those charges to oscillate up and down.  In the case of the long wavelength radiation the charge at right oscillates slowly.  This is low frequency and low energy motion.  The short wavelength causes the charge at right to oscillate more rapidly - high frequency and high energy.

The characteristics long wavelength - low frequency - low energy go together. So do short wavelength - high frequency - high energy.  Note that the two different types of radiation both propagate at the same speed.



This is really just a partial list of some of the different types of EM radiation.  In the top list, shortwave length and high energy forms of EM radiation are on the left (gamma rays and X-rays for example).  Microwaves and radiowaves are longer wavelength, lower energy forms of EM radiation.

We will mostly be concerned with just ultraviolet light (UV), visible light (VIS), and infrared light (IR).  Note the micrometer (millionths of a meter) units used for wavelength.  The visible portion of the spectrum falls between 0.4 and 0.7 micrometers (UV and IR light are both invisible).  All of the vivid colors shown above are just EM radiation with slightly different wavelengths.  WHen you see all of these colors mixed together, you see white light.

1.
 Unless an object is very cold (0 K) it will emit EM radiation.  All the people, the furniture, the walls and the floor in the classroom are emitting EM radiation.  Often this radiation will be invisible so that we can't see it and weak enough that we can't feel it.  Both the amount and kind (wavelength) of the emitted radiation depend on the object's temperature.

2.
 The second rule allows you to determine the amount of EM radiation (radiant energy) an object will emit.  Don't worry about the units, you can think of this as amount, or rate, or intensity.  Don't worry about σ either, it is just a constant.  The amount depends on temperature to the fourth power.  If the temperature of an object doubles the amount of energy emitted will increase by a factor of 2 to the 4th power (that's 2 x 2 x 2 x 2 = 16).  A hot object just doesn't emit a little more energy than a cold object it emits a lot more energy than a cold object.  This is illustrated in the following figure (which wasn't shown in class):

3.
 The third rule tells you something about the kind of radiation emitted by an object.  We will see that objects usually emit radiation at many different wavelengths.  There is one wavelength however at which the object emits more energy than at any other wavelength.  This is called lambda max (lambda is the greek character used to represent wavelength) and is called the wavelength of maximum emission.  The third rule allows you to calculate "lambda max."  This is illustrated below (also not shown in class):


 The graph below  also helps to illustrate the Stefan-Boltzmann law and Wien's law, particularly the meaning of lambda max.

Notice first that both and warm and the cold objects emit radiation over a range of wavelengths.  In some respects this is like quiz grades.  Not everyone in the room gets the same score; there's usually a very wide range of scores.  Objects do emit more of one particular wavelength than any other wavelength. This is lambda max. 

The area under the warm object curve is much bigger than the area under the cold object curve.  The area under the curve is a measure of the total radiant energy emitted by the object.  This illustrates the fact that the warmer object emits a lot more radiant energy than the colder object.

Lambda max has shifted toward shorter wavelengths for the warmer object.  This is Wien's law in action.  The warmer object is emitting a lot of short wavelength radiation that the colder object doesn't emit.
A bulb connected to a dimmer switch can be used to demonstrate the rules above (see p. 66 in the photocopied Classnotes).  We'll be interested in and looking at the EM radiation emitted by the tungsten filament in the bulb.

The bottom of p. 66 has been redrawn below for clarity:

We start with the bulb turned off (Setting 0).  The filament will be at room temperature which we will assume is around 300 K (remember that is a reasonable and easy to remember value for the average temperature of the earth's surface).  The bulb will be emitting radiation, it's shown on the top graph above.  The radiation is very weak so we can't feel it.  It is also long wavelength far IR radiation  so we can't see it.  The wavelength of peak emission is 10 micrometers.

Next we use the dimmer switch to just barely turn the bulb on (the temperature of the filament is now about 900 K).  The bulb wasn't very bright at all and had an orange color.  This is curve 1, the middle figure.  Note the far left end of the emission curve has moved left of the 0.7 micrometer mark - into the visible portion of the spectrum.  That is what you are able to see,  the small fraction of the radiation emitted by the bulb that is visible light (but just long wavelength red and orange light).  Most of the radiation emitted by the bulb is to the right of the 0.7 micrometer mark and is invisible IR radiation (it is strong enough now that you could feel it if you put your hand next to the bulb).

Finally we turn on the bulb completely (it was a 200 Watt bulb so it go pretty bright).  The filament temperature is now about 3000K.  The bulb is emitting a lot more visible light, all the colors, though not all in equal amounts.  The mixture of the colors produces a warm white light.  It is warm because it is a mixture that contains a lot more red, orange, and yellow than blue, green, and violet light.  It is interesting that most of the radiation emitted by the bulb is still in the IR portion of the spectrum (lambda max is 1 micrometer).  This is invisible light.  A tungsten bulb like this is not especially efficient, at least not as a source of visible light.

You were able to use one of the diffraction gratings to view all the colors that make up visible light. 
When you looked at the bright white bulb filament through one of the diffraction gratings the colors were smeared out to the right and left as shown below:

Some of the gratings behaved a little differently as shown below:

The sun emits electromagnetic radiation. That shouldn't come as a surprise since you can see it and feel it.  The earth also emits electromagnetic radiation.  It is much weaker and invisible.  The kind and amount of EM radiation emitted by the earth and sun depend on their respective temperatures.


The curve on the left is for the sun.  We first used Wien's law and a temperature of 6000 K to calculate  lambda max and got 0.5 micrometers.  This is green light; the sun emits more green light than any other kind of light.  The sun doesn't appear green because it is also emitting lesser amounts of violet, blue, yellow, orange, and red - together this mix of colors appears white.  44% of the radiation emitted by the sun is visible light,  49% is IR light (37% near IR + 12% far IR), and 7% is ultraviolet light.  More than half of the light emitted by the sun is invisible.

100% of the light emitted by the earth (temperature = 300 K) is invisible IR light.  The wavelength of peak emission for the earth is 10 micrometers. 

Because the sun (surface of the sun) is 20 times hotter than the earth a square foot of the sun's surface emits energy at a rate that is 160,000 times higher than a square foot on the earth.  Note the vertical scale on the earth curve is different than on the sun graph.  If both the earth and sun were plotted with the same vertical scale, the earth curve would be too small to be seen.
We saw earlier that tungsten bulbs produce a lot of wasted infrared light (wasted in terms of not lighting up a room).  They also produce a warm white color.  Energy efficient compact fluorescent lamps (CFLs) are designed to mimic the visible light output of a tungsten bulb without producing a lot of wasted infrared light.  CFLs come with different color temperature ratings. 

The bulbs with the hottest temperature rating (5500 K ) in the figure above emits more purples, blues, and greens and produces a cooler, bluish white.  This is much closer to the light emitted by the sun. 

The tungsten bulb (3000 K) and the CFLs with temperature ratings of 3500 K and 2700 K produce a warmer white. 

Three CFLs with the temperature ratings above were set up in class so that you could see the difference between warm and cool white light.

You can see a clear difference between the cool white bulb on the left in the figure below and the warm white light produced by a tungsten bulb (2nd from the left) and 2 CFCs with low temperature ratings (3rd and 4th from the left).  This figure is from an article on compact fluorescent lamps in Wikipedia.