Mon., Oct. 1 notes

Monday Oct. 1, 2007

The 2nd optional assignment was collected in class today. A new optional assignment was handed out. It will be due at the beginning of class next Monday (Oct. 8). This new optional assignment will give you some practice with questions on electromagnetic radiation.

The Experiment #2 reports and the revised Expt. #1 reports are both due next Monday. Experiment #2 doesn't take long to perform, you should plan on returning the materials this week so that you can pick up the supplementary information sheet.

About 2/3rds of the 1S1P Assignment #1 reports have been graded and were returned in class today.

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 now have most of the tools we will need to begin to study energy balance on the earth. It will be a balance between incoming sunlight energy and outgoing energy emitted by the earth. We will look at the simplest case, first, the earth without an atmosphere (or at least an atmosphere without greenhouse gases)

You might first wonder how, with the sun emitting so much more energy than the earth, it is possible for the earth to be in energy balance with the sun. The earth is located about 90 million miles from the sun and therefore only absorbs a very small fraction of the energy emitted by the sun.

To understand how energy balance occurs we start, in Step #1, by imagining that the earth starts out very cold and is not emitting any EM radiation at all. It is absorbing sunlight however so it will begin to warm.

Once the earth starts to warm it will also begin to emit EM radiation, though not as much as it is getting from the sun (the slightly warmer earth in the middle picture is now colored blue). Because the earth is still gaining more energy than it is losing the earth will warm some more.

Eventually it will warm enough that the earth (now shaded greenish brown) will emit the same amount of energy (though not the same wavelength energy) as it absorbs from the sun. This is radiative equilibrium, energy balance. The temperature at which this occurs is 0 F. That is called the temperature of radiative equilibrium. You might remember this is the figure for global annual average surface temperature on the earth without the greenhouse effect.

Next we are going to see that the atmosphere behaves somewhat differently, when it comes to emitting and absorbing electromagnetic radiation, than the earth or the sun. We will need to understand, in particular, how the atmosphere filters incoming sunlight and outgoing IR radiation emitted by the ground.

In some respects the earth and the sun behave just like the tungsten filament in the light bulb used in the class demonstration. Both the earth and the sun emit continuous spectra. Part of the light emitted by the sun falls in the visible part of the spectrum. If you were to look at the sun (something you shouldn't do of course) with one of the diffraction gratings handed out in class you would see all the colors of visible light. There wouldn't be any gaps or colors missing. This is shown again at the top of the figure below.

Gases behave differently. We looked at the visible light emitted by helium (a high-voltage power supply was need to heat the helium so that it would be hot enough to emit visible light). Rather than a continuous spectrum, the helium emitted only certain wavelengths. This is called a line spectrum. Helium contains only two electrons and is a relatively simple atom and its line spectrum was also fairly simple.

Neon (Ne) also emitted a line spectrum, thought there were more lines at different wavelengths.

Finally we looked at the visible light emitted by molecular nitrogen. In this case the spectrum was somewhere in between a continous spectrum and a line spectrum. You were able to see bands of colored light rather than clear line emitted by the nitrogen (the bands are probably very closely spaced lines).

This is closer to being a continous spectrum but there were still gaps, wavelengths without any emissions.

In the same kind of way, air absorbs some wavelengths and transmits others. We will need to worry about the filtering effect of the atmosphere on ultraviolet, visible, and infrared light because all three types of light are found in sunlight.

We will first look at the effect simple blue, green, and red glass filters have on visible light. This figure wasn't shown in class.

If you try to shine white light (a mixture of all the colors) through a blue filter, only the blue light passes through. The filter absorption curve shows 100% absorption at all but a narrow range of wavelengths that correspond to blue light. Similarly the green and red filters only let through green and red light.

The following figure is a simplified easier to remember representation of the filtering effect of the atmosphere on UV, VIS, and IR light (found on p. 69 in the photocopied notes)

0% absorption means the atmosphere behaves like a window made of clear glass, the air is transparent to light. The light can pass freely through the atmosphere. 100% absorption on the other hand means the atmosphere is opaque to light, it blocks the light by absorbing it.

In our simplified representation oxygen and ozone make the atmosphere a pretty good absorber of UV light The atmosphere is pretty nearly perfectly transparent to VIS light (we can check this out with our eyes, we can see through the air, it is clear).

Greenhouse gases make the atmosphere a selective absorber of IR light - it absorbs certain IR wavelengths and transmits others. It is the atmosphere's ability to absorb (and also emit) certain wavelengths of infrared light that produces the greenhouse effect and warms the surface of the earth.

Note "the atmospheric window" centered at 10 micrometers. Light emitted by the earth at this wavelength will pass through the atmosphere. Another transparent region, another window, is found in the visible part of the spectrum.

The following figure found at the top of p. 70 in the photocopied Class Notes is a more realistic filter absorption for the atmosphere.