# Oil Spot Photometer

When an oil spot on a card is illuminated equally from both sides, it mysteriously disappears. This allows you to compare the brightness of the light sources on either side of the card.

- cooking oil (any type will work)
- a white index card (e.g., 4 x 6 inches or 3 x 5 inches)
- paper towel or tissue (not shown)
- two identical, new 60-watt frosted incandescent light bulbs
- two power strips and plug-in lamp sockets (or other safe light sockets without a shade or reflector that will hold a bare light bulb vertically)
- extension cord(s) as necessary to allow both lights to be placed on a table or other flat surface about 3 feet (1 meter) apart (not shown)
- a pot holder or towel for handling hot bulbs (not shown)
- a ruler, meter stick or measuring tape
- a 40-watt frosted incandescent light bulb
- a 75-watt frosted incandescent light bulb
- a compact fluorescent light bulb that fits a standard socket and is intended to replace a 60-watt incandescent bulb (not shown)
- an LED lamp that fits a standard socket and is intended to replace a 60-watt incandescent bulb (not shown)
- optional: masking tape

*Note: Keep on hand the packaging that the light bulbs came in, which contains information about power (watts) and illumination (lumens).*

- Pour a very small amount of cooking oil into the lid of the container holding the oil.
- Dip a fingertip into the oil, then carefully smear it against the middle of the white card, forming a round oil spot approximately 1/2 inch to 1 inch (one or two centimeters) in diameter. Use a paper towel or tissue to blot any excess oil and wipe your finger, but be careful not to smear oil anywhere else on the card.
- Place the two 60-watt incandescent bulbs into the power strips or other sockets. Use your measuring tape or meter stick to position the lights in a straight line so that the centers of the bulbs are six ft (two m) apart. If you’re short on space, they can be as close as three ft (one m) apart, but six feet is better. If necessary, use the masking tape to secure the lights in place.
- Turn on both lights.

Position yourself so you are next to the table, between the two lights but not blocking either of them. Hold the card upright directly in the path between the lights, so that each side of the card faces one of the lights. Adjust your position slightly so you are looking at only one side of the card.

Move the card along the path between the lights so that it is first closer to one light and then the other, keeping your eye on only one side of the card. What happens to the darkness and lightness of the oil spot (compared to the rest of the card) as you move the card back and forth? When is the spot darker than the rest of the card? When is it lighter?

Notice that there is a location between the lights where the oil spot comes close to disappearing. Move the card to this location, and mark or take note of the distance relative to the two lights.

Replace the two 60-watt light bulbs with the 40-watt and 75-watt bulbs (use the pot holder or towel if the lights are hot). As before, find the position between the lights where the oil spot disappears, and notice the location of the card relative to the two lights.

Replace the 40-watt and 75-watt bulbs with a 60-watt incandescent bulb and the compact fluorescent bulb that is designed to serve as a replacement for a 60-watt incandescent bulb. (*Note: you may have to let the fluorescent bulb warm up for a short time to achieve full brightness.*) Again, find the position between the lights where the oil spot disappears, and take note of the card's location relative to the two lights. Hold your hand above each of these bulbs. It should be easy to feel that the incandescent bulb is much hotter than the fluorescent bulb. Now take a look at the packaging for both bulbs, and notice the power (watts), illumination (lumens), and price for each bulb. (If the prices aren’t printed on the boxes, see if you can find out what they are.)

Finally, compare the LED bulb with the 60-watt incandescent bulb and compare the illumination (lumens) listed for each bulb.

Compared to the normal white surface of the card, the oil spot can reflect less light or transmit (let pass through) more light, depending on the distance of the light source.

When the amount of light shining on the side of the card you are looking at is greater than the light shining on the other side, more light is reflecting from the rest of the card than from the oil spot, and the amount passing through the spot toward you from the dimmer side isn’t enough to make up the difference. As a result, the oil spot appears darker than the rest of the card.

When the side of the card you are looking at is illuminated less than the other side of the card, there is still more light reflecting from the rest of the card than from the oil spot, but the amount passing through the spot toward you from the brighter side is more than enough to make up the difference. As a result, the oil spot appears lighter than the rest of the card.

The oil spot disappears when it is equally illuminated from both sides. In this case, the light transmitted through the oil spot is equal to the light reflected from the card. For the two 60-watt bulbs, this point should be about halfway between the two bulbs, since they should be providing approximately equal illumination. For the 40- and 75-watt bulbs, however, the location where the spot disappears should be noticeably closer to the 40-watt bulb. The dimmer the light source, the closer you have to be to it to receive a given amount of illumination.

For the 60-watt incandescent bulb and the fluorescent “60-watt replacement” bulb (once it's warmed up), the card should again be approximately halfway between the two bulbs when the oil spot disappears, showing that the two lights are of approximately equal brightness. Fluorescent bulbs are more efficient than incandescent bulbs, converting a greater percentage of electrical energy into light rather than heat.

According to normal ratings, a fluorescent bulb uses 16 watts of electricity to give a light output of 800 lumens, whereas an incandescent bulb uses 60 watts of electricity to give a light output of 855 lumens. The fluorescent bulb gives about 90 percent of the light output of the incandescent bulb, but uses only about 25 percent as much energy to do it.

Here are a few other variations on this activity you may want to try:

**Double Bright**

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*):

$$I = \frac{P}{A}$$

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

$$A = 4 \pi r^2$$

So for a bulb of constant power (*P*), the intensity is

$$I = \frac{P}{A} = \frac{P}{4 \pi r^2}$$

Because *r*^{2} 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*:

$$\frac{P_1}{4\pi {r_1}^2} = \frac{P_2}{4\pi {r_2}^2}$$

and

$$\frac{P_1}{P_2} = \frac{{r_1}^2}{{r_2}^2}$$

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* = 2*P1)*, then

$$\frac{P_1}{P_2} = \frac{1}{2} = \frac{r_{12}}{r_{22}}$$

and

$$\frac{r_1}{r_2} = \frac{\sqrt{1}}{\sqrt{2}} = \frac{1}{1.4}$$

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.