Abstract
Have you ever noticed how the moon appears bigger at the horizon, just as it is rising over the treetops, than it does later in the evening when it is overhead? Actually, the size of the moon does not change, but our perception of its size changes based on where it is in the sky. In this human biology science fair project, you will investigate Emmert's law, which explains the full moon illusion. You will estimate the size of the perceived increase in the size of the moon at the horizon.Objective
In this human biology science fair project, you will investigate Emmert's law, which is the basis for the full moon illusion.
Introduction
A full moon rising over the horizon often appears to be unusually large. Many people will sat that the moon gets smaller as it moves higher up in the sky above the horizon. Actually, the angular size of the moon, which is about 0.5 degrees, is the same wherever it is in the sky. For comparison, the tip of your little finger, when your hand is held at arm's length, is about 1 degree. Angular size is measured in degrees, with 360 degrees equaling a full circle. An object's angular size is the angle between the lines of sight to its two opposite sides. For example, the angular size of the sky is about 180 degrees. An object's angular size is a measure of how large the object actually appears to be, which depends on both actual size and the distance to the object. This example is familiar to everyone: an object that is near to you appears larger (that is, it has a larger angular size) than when it is farther away from you.
What is the basis for this full moon illusion? It is not that the moon appears larger on the horizon because it's seen next to things like trees and houses, since airline pilots flying at very high altitudes sometimes experience the moon illusion without any objects in the foreground. The answer is that your brain "thinks" the region of the sky overhead is closer than the region of the sky at the horizon, so it adjusts the size of the moon's image accordingly. Think about it: birds, clouds, and airplanes flying overhead seem closer than birds on the horizon do. When the moon is near the horizon, your brain miscalculates the moon's true distance and size.
One way to explore this phenomenon is with afterimages. An afterimage is the image you see when you look at a brightly colored object and then look away. It is caused by fatigue of your cone cells. There are three types of cone cells, loosely called blue, green, and red, depending on which type of light they respond to best. When you look at a red object, for example, the red cone cells are preferentially stimulated. The stimulation of the red cone cells causes them to send a message to the brain, saying, in effect, "the color of the object is red."
Prolonged exposure to a particular color can cause cone cell fatigue. For example, if you stare at a red object, the red cones become fatigued and temporarily unable to respond. If you look at a white area after staring at a red image, you will see an afterimage that is the same size and shape as the original, but a different color. Try this by looking at the red circle in Figure 1 for 30 seconds, then looking at the white region to the right. Can you see the blue-green afterimage?
Why is the afterimage blue-green? When you look at the white surface after staring at the red object, your eyes will essentially receive equal doses of red, green, and blue light, but only the blue and the green cones are able to respond. Because of cone cell fatigue, the input from the red cones is missing from the region of the afterimage. So you see the afterimage as blue-green.
The afterimage disappears over time because the red cone cells recover from their fatigue and become active again. When the red cone cells are active again, all three types of cone cells respond to the white surface, and you see the white region normally.
How can we use afterimages to explore the full moon illusion? The actual size of the image on your retina, caused by staring at the colored circle in Figure 1, does not change. But, as you will see in this experiment, the perceived size of the afterimage depends on the distance between you and the surface on which you view the afterimage. In other words, the perceived size of the afterimage varies directly with the distance of the surface on which it is viewed. This relation is an instance of a more general perceptual relation, known as Emmert's law, which states: The perceived size of a particular visual angle is directly proportional to its perceived distance.
You will use Emmert's law to study the full moon illusion. How much bigger does the moon appear to be at the horizon? In other words, what is the magnitude of the moon illusion? In this human biology science fair project, you will estimate the size of the brain's miscalculation in the full moon illusion.
Terms, Concepts and Questions to Start Background Research
Bibliography
Materials and Equipment
Experimental Procedure
Part 1: Evaluating Afterimage Size in Relation to Distance of the Viewing Surface
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| Figure 1. Look at the red circle for 30 seconds, and then look at the white circles on the right side. Move your head closer or farther from the screen. How does the size of the afterimage change? |
Part 2: Evaluating Afterimage Size in Relation to Perceived Distance to the Horizon and the Zenith
In Part 1, you established how the size of the afterimage depends on the perceived distance to the surface upon which it is viewed. You can use this same method to determine how your brain perceives the relative distances of the horizon and the zenith, which is the region of the sky directly overhead. To do this, you will "acquire" an afterimage, then look at the horizon and at the zenith. The perceived change in the size of the afterimage reflects the perceived difference in the distance to the horizon and to the zenith.
This part requires you to find an outside area with a clear view of the horizon and the zenith. Don't try it at noon, when the Sun is directly overhead, since this interferes with your observation of the afterimage at the zenith. Mid-morning or evening is probably best. And the day should be fairly cloudless with a lot of blue sky to look at.
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| Figure 2. Use the blue square to form an afterimage, then look at the horizon and the zenith. Does the size of the afterimage appear to change? |
Part 3: Estimating Size of the Afterimages Perceived at the Horizon and at the Zenith
In Part 3, you will use different-sized squares to estimate the relative size of the afterimages perceived at the horizon and at the zenith. The idea is to learn what different relative sizes look like and then apply that learning to estimating the relative sizes of the horizon and zenith afterimages. The image (and the Sun) looks bigger on the horizon than it does at the zenith, but by how much? So if we say it is size "1" at the zenith, what is it at the horizon? Is it 1 1/2 times larger? Is it twice as large? The goal is to assign an approximate numerical value to the size of the full moon illusion.
Variations
Credits
David B. Whyte, PhD, Science Buddies
This project is based on the following article:
Gruber, Howard E., King, William L. (1962, March 30). Moon Illusion and Emmert's Law. Science, Vol. 135, 1125-1126. Retrieved August 1, 2008, from http://www.sciencebuddies.org/science-fair-projects/project_ideas/HumBio_FullMoonIllusion.pdf
Last edit date: 2008-11-07 10:08:00
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