We have spent a good deal of time in class discussing "blackbody" radiation: the way it is emitted by all objects at a finite temperature, the way the total power emitted per unit area by an object is proportional to the fourth power of the absolute temperature, and the way some objects are more perfect emitters of radiation than others. This experiment is an opportunity to explore some of these ideas using a simple radiometer, an instrument which measures the total radiation power collected by its detector.

The Radiometer

The detector in the Daedalon EG-45 Radiometer is an evaporated thin-film resistor array which changes its electrical resistance with temperature. The "thermal mass" is very small so there is very little lag time in the response of the instrument. The thin-film resistor is carefully "blackened" so that it absorbs radiation uniformly from the ultraviolet to the far infrared. The detector is enclosed in a small case filled with argon gas and having a window cut from a potassium bromide crystal. This window transmits radiation into the far infrared region of the spectrum. The detector case is mounted in a massive aluminum housing to reduce rapid temperature changes. The detector measures the radiation balance between the source temperature and its own temperature, so it is important to keep the detector at a constant temperature while making a measurement.

The aperture where radiation enters to fall on the detector is conical with a 60-degree acceptance angle. At the end of the cone is a shutter which is closed in front of the detector while adjusting the zero of the meter scale. The shutter is closed when the actuator rod is down, and open when it is pulled up as far as possible- look into the aperture while operating the shutter actuator to be sure you understand this. The shutter is enclosed in the aluminum housing so that it has the same temperature as the detector.

Radiant energy or "irradiance" is usually measured in watts/meter². One w/m² is quite a small unit. The solar irradiance at the top of the earth's atmosphere measured normal to its direction is about 1,400 w/m². The amount that reaches the earth's surface is only a fraction of that for most of the year.

Instrument Operation

The measurement range of the radiometer is quite wide, from direct sunlight to the warmth of a hand print left on a table. For intense sources such as the sun or heaters where the source is much warmer than the instrument, measurements are very easy. When the source is close to the instrument's temperature or even cooler than the instrument, additional care must be used.

1. Set the instrument on a stable support facing the source and plug it into the power line. Try not to have reflecting surfaces that might confuse the direct measurement.
2. Turn on the radiometer. It stabilizes very quickly and has very little drift. Leave it on through the lab period.
3. Set the ZERO ADJUST knob so that the meter reads zero. The zero changes from scale to scale and should be set each time the RANGE switch is changed. Get in the habit of checking the zero just before you open the shutter to make a measurement. In some cases, if the source being measured can be switched on and off, it might be better to zero the radiometer with the shutter open and the source off and then turn the source on for the measurement.
4. Point the radiometer at the source to be measured. Lift the shutter actuator to open the shutter. Note the deflection of the meter. If it is off-scale or very low, change the RANGE switch, then close the shutter to recheck the ZERO and try again, until you get a satisfactory meter deflection- above one, but not off-scale.
5. The instrument reads in watts/meter². The RANGE switch indicates the full-scale value, so that a reading of 10 on the Range 100 scale would be 100 w/m².
6. The collection angle of radiation is a 60-degree cone (0.8 steradians) so when measuring uniform sources of radiation they should be arranged to fill the acceptance angle of the instrument. With small sources such as light bulbs this is less significant and the inverse square law governs the decrease in radiation with increased separation between the source and instrument. When measuring a distance to the instrument, the shutter actuator is in the plane of the detector.

Procedure (DO NOT READ THIS UNTIL YOU HAVE READ THE ABOVE!)

With the radiometer set to its most sensitive range and the ZERO adjusted, point the instrument at a flat black paper surface and open the shutter. The reading should be very low- as the paper is essentially the same temperature as the shutter. Try a piece of white paper and note the difference. For both black and white surfaces, try tilting the paper around to reflect the room lights into the radiometer and see which paper is least sensitive to this reflection.

Now warm the paper up by holding your hand against the back of it while you place it in front of your radiometer. Can you see a difference? Does the warm paper emit more radiation? Try this experiment with the wall or the bench top: measure the radiation flux at room temperature then, without changing the location of the instrument, warm the surface with your hand and measure it again. Can you see a difference? Of course, this is not a quantitative experiment, but it gives you some feeling for the sensitivity of the instrument to small changes in the radiation emitted by surfaces as their temperature changes.

Now compare the relative emissivity of a variety of surfaces at the same temperature. You have a metal container with three regions which have been prepared differently: One is shiny metal, one is painted white, and one is painted black. Pick the container up only with a paper towel or at the very top so that your greasy fingerprints do not change its emissivity! Using hot water from the sink, fill your container about 3/4 full, and wait a brief time for the metal to come to the same temperature as the water. Do not get the sides of your container wet, and be especially careful not to spill water on the radiometer! Position the container in front of the radiometer so that one face of the container fills the aperture cone of the radiometer. Record the radiation emitted by each of the faces of the container in turn as you rotate it. Go through the cycle of measurements 3 times to get some feeling for the uncertainty of the measurement. Do not forget to record the UNITS associated with your measurements. Do your radiation readings drop as the water slowly cools off?

Since the surfaces are the same temperature, the differences in radiation measured result from differences in the EMISSIVITY of the surface material. In principle, surfaces which are highly absorbing (low reflectance) should also be highly emitting. Do you observe this? "Rank" your three surfaces in order of reflectance as best you can, and see how this correlates with your measured emission. (Of course, you are estimating the reflectance in the visible spectrum but measuring the emissivity in the infrared, so they are not quite the same thing.) Write enough to make your results and your interpretation clear- not just a table of numbers left for the reader to guess what you mean.

The radiometer can also be used to explore the relationship between the local irradiance or brightness of a source, the intrinsic luminosity, and the distance between source and detector. You have a small light bulb mounted at the end of a board and connected to a power supply through a switch so that it can be turned on and off. Experiment with this to be sure that you understand how it works. Set the power supply to 12 volts. Read the scale on the volt meter, not the knob. Do not go above 12 volts or the light bulb will burn out!

Using the radiometer, measure the brightness of the light bulb in watts/meter² at various radial distances r between the lamp filament and the radiometer detector, say r = 0.1, 0.2, 0.3, 0.4, 0.5 meters. Slide the radiometer down the board so that the side of the lamp "seen" by the radiometer is always the same (explain why this is a good idea). For these measurements, "zero" the radiometer with the shutter open and the lamp off. Be careful that you do not allow the radiometer to see your warm hands or other body parts, or those of other people in the room. On the graph paper, plot the brightness in watts/meter² vs 1/(4*pi*r²). Would you expect the plotted points to lie on any lind of line? From the properties of this line, if any, determine the luminosity, L, of your light bulb, in watts. Comment on the physical reasonableness of your result. Does the brightness appear to "fall off like 1/r²" the way we have discussed it for stars? The power delivered to the lamp by the power supply (in watts) is the product of the voltage across the lamp (in volts) and the current through the lamp (in amps). How many watts are you delivering to your lamp? (Beware- the amp meter displays the current used by you and your neighbors down the table!) How does this compare with the power radiated by your lamp? Give a possible reason for any significant difference.

Most of the first part of this writeup was edited from the manual for the radiometer prepared by the Daedalon Corporation.