Here are a few other variations on this activity you may want to try:
What happens if you use a single 60-watt bulb on one side and two 60-watt bulbs on the other side? Where will the oil spot disappear? Try predicting the location of the "equal point" using this hint: Brightness varies inversely with the square of the distance from the light source. Then set up the bulbs this way and test your prediction. (See Box o’ Math below for an explanation.)
A Bright Idea
How much brighter is the 75-watt bulb than the 40-watt bulb? Use your photometer and the inverse-square relationship cited above to figure this out.
How Much Dimmer?
Use your photometer to test the relative light output of bulbs that have the same wattage but differ in some other way (e.g., a new bulb and a bulb that’s been used for awhile, two different brands or shapes of bulb, or a standard bulb and a “soft white” bulb).
Light and Power
On the bulb packages, light output is given in lumens. In incandescent bulbs, are lumens and watts proportional? Would twice the wattage give twice the light output? How are lumens and watts related? Look up lumen and the related units candela and lux.
How Bright Is the Sun?
You can even use your photometer to calculate the brightness of the sun. You'll need to do this on a very sunny day using direct sunlight (Caution: Never look directly at the sun!) and you'll need a light source that has an output equivalent to or greater than a 200-watt incandescent bulb (see photo below). Watch the video above to see how we like to set this up.
Box o’ Math: The Inverse Square Law
The intensity of a light (I) which the human eye sees as brightness is equal to the light power (P) per unit area (A):
I = P/A
As light moves outward from a bulb, the power spreads over a spherical area of radius r that increases as the square of the distance from the bulb. The area (A) of a sphere with radius r is
A = 4πr2
So for a bulb of constant power (P), the intensity is
I = P/A = P/4πr2
Because r2 is in the denominator of the fraction, it’s verbally described as an inverse square. When the oil-spot card held between two light sources reaches the point of equal brightness, the intensities of the two lights are the same: I1 = I2 since the power of one light is P1 and the power of the other is P2, while the distance from the center of one light to the card is r1 and from the other light is r2:
P1/4πr12 = P2/4πr22
P1/P2 = r12/r22
The above equations let us calculate the distances at which two lights of different powers will balance. For example, if the second light is twice the power of the first (P2 = 2P1), then
P1/P2 = 1/2 = r12/r22
r1/r2 = √1/√2 = 1/1.4
The distance to the brighter light is 1.4 times the distance to the dimmer light. Light is one of many phenomena that vary inversely with the square of the distance from the source. Other phenomena that follow an inverse square law include sound, magnetism, and gravity.