This is meant to be handed out to the students.
* Footnote: Let's put this in some other forms. Since there are 1,000 meters in a kilometer and 100 centimeters in a meter, the distance to the Sun in centimeters is = 150,000,000 X 1,000 X 100 = 15,000,000,000,000 cm. A good shorthand is to write this distance as = 15 x 10 cm. Where you simply count the number of zeros and place them in the exponent after the 10. This is called scientific notation and sure makes life easier.
But we're not going to stop here. Using the same technique used to get the wattage of the Sun, you will also determine the wattage of a very small light bulb. The reason for this is that we will then take this very small light bulb up to Yerkes Observatory and compare it to stars in the sky. It will be our reference standard. Astronomers sometimes call such things "standard candles," so that's what we'll call it. Once we know it's wattage along with how far away it is, we will be able to get the distances of a star like the Sun, by simply assuming that the star is the same wattage as the Sun. It seems odd, but with just a couple of measurements today, we will be all set to determine some of the greatest distances in the Universe.
[Intensity of source of light at a distance] =[Power output of source]/[Distance to source]
Written as symbols this is: I = W/D
To use this equation today, we will want to solve for W. That is actually very simple. All we have to do is multiply both sides of the equation by D. Thus, the wattage of the sources of light we are investigating is simply W = ID. This would be great if we could just directly measure I, the intensity. Well, it's not that easy. What is simple, however, is to compare the light from two sources and determine that the intensity is the same from both sources. So, we'll build a comparison photometer to tell us when the light from two sources is the same. That way, if we know the wattage and two distances, we can solve for the other unknown wattage.
It works like this: Suppose we have two sources of light that are in the right place to emit the same amount of light. If source number 1 is given by the equation below with 1's in parentheses and the quantities for source 2 are shown with 2's in parentheses, then: I(1) = W(1)/D(1) and I(2) = W(2)/D(2)
But, since we will match the two intensities so that they are equal with the comparative photometer, then I(1) = I(2). This allows us to write just one equation from two, but setting the I's equal to one another. We get W(1)/D(1) = W(2)/D(2)
This equation allows us to solve for a wattage (W(2)) if we know the two distances and the wattage of source 1 (W(1)). All we have to do is multiply by the denominator on the right side. That gives us the final equation we will use today. [W(1)/D(1)] * D(2) = W(2)
Recall how the different symbols are defined:
W(source) = the power output of "source" -- units are watts
D(source) = distance from photometer to "source" -- units are centimeters
I(source) = intensity of light from "source" -- units are watts/(cm2)
Record your observations, computations and results in this table. Note that you must repeat your observations four times for each set of sources. Average your final results for each of the three unknown sources and write the final answers in the table at the bottom of the page
source 1 D(source 1) D(source 1)^2 I(source 1) = (cm) (cm^2) W(1)/D(1)^2. (Watts/cm^2) 100 watt bulb trial 2 trial 3 trial 4 200 watt bulb trial 2 trial 3 trial 4 100 watt bulb trial 2 trial 3 trial 4 source 2 D(source 2) D(source 2)^2 W(source 2) = (cm) (cm^2) I(1)*D(2)^2. (Watts) 2 bulbs together trial 2 trial 3 trial 4 Sun trial 2 trial 3 trial 4 "standard candle" trial 2 trial 3 trial 4Summary Results (Average wattage) for each source:
Important Disclaimers and Caveats