Monday Feb. 25, 2013
click here to download today's notes in a more printer friendly format

You heard "Lover's Carvings" from Bibio before class.  It was something I heard watching TV over the weekend.  I was too busy playing with my new laser pointers to spend much time thinking about music for today.

The Experiment #2 reports were collected today.  It will take a week or so to get them all graded so you should expect to get them back sometime next week.

The Upper Level Chart Optional Assignment has been graded.  If you missed 3 pts or less you got a Green Card.  Everyone got extra credit (0.5 pts).  I hope to have the CO2 reports graded by Wednesday (Friday at the latest).  I'm also working still on the Surface Weather Map Analysis.

I am now the owner of a red, green, and purplish blue laser pointer.  They're bright and you can see them on the screen even when the projector is on.  I projected the left figure below onto one of the projector screens and pointed each of the laser pointers so that its light would fill the proper circle below (purple-blue in the 405 nm circle, green in the 532 nm circle, and red in the 650 nm circle).   Note nanometers (nm) are billionths of a meter and is just another type of unit that you can use for wavelength; 405 nm is the same as 0.405 µm.

The picture at right below (from Wikipedia) gives you a pretty good idea of what the light from each laser pointer looked like. 




What I really wanted to do was to orient the laser pointers so that the spots of light would fall on top of each other.  We should get something that looks white because mixing all the colors of visible light together produces white light.  The resulting spot of light was pretty small but did look whitish (one problem is that the intensities of the laser pointers are different).

Here's another illustration of how mixing red, green, and blue light produces white light (again from Wikipedia)



A good question came up at the end of Friday's class.  "If white light is a mixture of all the colors, why, when you mix together a bunch of different colors of paint, does the mixture turn black"?

It might be easiest to explain (and demonstrate) with filters.



A red filter will only let red light through (the other colors are absorbed), a green filter transmits only green light.  When you put the red and green filters back to back nothing gets through.

Paint is similar except it involves reflection instead of transmission (absorption is involved in both cases).

The pigments in green paint absorb everything except for green.  Green is reflected.


Red paint absorbs everything except for red.  When you paint an object with both red and green (and all the other colors just to play it safe) everything is absorbed.  No light is reflected and the object appears black.  For the bottom figure I took the 7 colored pencils used to draw the 7 rays of colored light and colored in the square.  The result is not exactly black but it is headed in that direction.  Grab some colored pencils and try it yourself.

We spent most of the rest of the class learning about some rules governing the emission of electromagnetic radiation.  Here they are:

1.
Everything warmer than 0 K will emit EM radiation.  Everything in the classroom: the people, the furniture, the walls and the floor, even the air, 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 (or perhaps because it is always there we've grown accustomed to it and ignore it).  Both the amount and kind (wavelength) of the emitted radiation depend on the object's temperature.  In the classroom most everything has a temperature of around 300 K and we will see that means everything is emitting infrared (IR) radiation with a wavelength of about 10µm.

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 (though they're given in the figure below), you can think of this as amount, or rate, or intensity.  Don't worry about σ (the Greek character rho) 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:


The cool object is emitting 2 arrows worth of energy.  This could be the earth at 300 K.  The warmer object is 2 times warmer, the earth heated to 600 K.  The earth then would emit 32 arrows (16 times more energy).

The earth has a temperature of 300 K.  The sun is 20 times hotter (6000 K).  Every square foot of the sun's surface will emit 204 (160,000) times more energy than a square foot of the earth's surface.

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 but not in equal amounts.  But, objects emit more of one particular wavelength than any of the others.  This is called  λmax ("lambda max", lambda is the greek character used to represent wavelength) and is the wavelength of maximum emission.  The third rule allows you to calculate  λmax. The tendency for warm objects to emit radiation at shorter wavelengths is shown below.


The cool object is probably emitting infrared light (that would be the case for the earth at 300 K) so the 2 arrows of energy are colored red.  The warmer object will also emit IR light but also shorter wavelengths such as yellow, green, blue, and violet (maybe even some UV if it's
hot enough).   Remember when you start mixing different colors of visible light you get something that starts to look white.

The graphs at the bottom of p. 65 in the photocopied ClassNotes also help to illustrate and explain the Stefan-Boltzmann law and Wien's laws.  We're really beating this topic to death and we're not done yet.



1.
Notice first that both and warm and the cold objects emit radiation over a range of wavelengths (the curves above are like quiz scores, not everyone gets the same score, there is a distribution of grades).  The warm object emits all the wavelengths the cooler object does plus lots of additional shorter wavelengths.

2.
The peak of each curve is λmax.  Note that λmax has shifted toward shorter wavelengths for the warmer object.  This is Wien's law in action.  The warmer object is emitting lots of types of short wavelength radiation that the colder object doesn't emit.

3.
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.


And next a demonstration of the Stefan-Boltzmann and Wien's Laws.  It consisted of an ordinary 200 W tungsten bulb is connected to a dimmer switch (see p. 66 in the photocopied ClassNotes).  We'll be looking at the EM radiation emitted by the bulb filament.



The graph at the bottom of p. 66 has been split up into 3 parts and redrawn for improved 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.  The wavelength of peak emission is 10 micrometers which is long wavelength, far IR radiation so we can't see it. 

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 were able to see, just 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 got 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 handed out in class to separate the white light produced by the bulb into its separate colors.

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 at left below.








Some of the gratings handed out in class behaved a little differently and spread out the colors horizontally, vertically, and diagonally (right sketch above)

Here are the rules for the amount and kind (wavelength of peak emission) of radiation emitted by an object.


Let's look at the light emitted by the sun and the earth.



The curve on the left is for the sun.  We have used Wien's law and a temperature of 6000 K to calculate λmax 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,  Very nearly half of sunlight (49%) is IR light (37% near IR + 12% far IR).  7% of sunlight is ultraviolet light.  More than half of the light emitted by the sun (the IR and UV light) 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 the sun's surface emits energy at a much higher rate than 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.

In the demonstration in class last Friday we also learned that ordinary tungsten bulbs (incandescent bulbs) produce a lot of wasted energy.  This is because they emit a lot of invisible infrared light that doesn't light up a room (it will warm up a room but there are better ways of doing that).  The light that they do produce is a warm white color (tungsten bulbs emit lots of orange, red, and yellow light and not much blue, green or violet). 

Energy efficient compact fluorescent lamps (CFLs) are being touted as an ecological alternative to tungsten bulbs because they use substantially less electricity, don't emit a  lot of wasted infrared light, and also last longer.  CFLs come with different color temperature ratings.



The bulb with the hottest temperature rating (5500 K ) in the figure above is meant to mimic or simulate sunlight (daylight).  The temperature of the sun is 6000 K and lambda max is 0.5 micrometers.  The spectrum of the 5500 K bulb is similar.

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.  Personally I find the 2700 K bulb "too warm," it makes a room seem gloomy and depressing (a student in class once said the light resembles Tucson at night).   The 5500 K bulb is "too cool" and creates a stark sterile atmosphere like you might see in a hospital corridor.  I prefer the 3500 K bulb in the middle.

The figure below is from an article on compact fluorescent lamps in Wikipedia for those of you that weren't in class and didn't see the bulb display.  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 (the 2 bulbs at right).



There is one downside to these energy efficient CFLs.  The bulbs shouldn't just be discarded in your ordinary household trash because they contain mercury.  They should be disposed of properly (at a hazardous materials collection site or perhaps at the store where they were purchased).

It probably won't be long before LED bulbs begin to replace tungsten and CFL bulbs.  The price has dropped significantly in just the last 6 months or so.