Seeing Science: Solving the Mystery of the Shrinking Moon

A perception problem from Science Buddies

Key concepts
Perception
Optical illusions
Human biology
Space

Introduction
Have you ever noticed how the moon appears much bigger at the horizon, just as it is rising over the nearby buildings or treetops, than it does later in the evening when it is directly overhead? Of course, the moon’s size does not change, but our perception of its size changes based on its position in the sky. In this activity you'll investigate Emmert's law, which helps explain the full-moon illusion, and estimate the size of the perceived increase in size of the moon when it is near the horizon. Then you could check out the real moon and see how this activity holds up to the full-moon illusion.

Background
A full moon rising over the horizon often seems to be unusually large, but looks smaller as it moves up in the sky. The actual size of the moon stays the same. So what is the basis for this illusion? One well-supported theory is that the brain "thinks" the sky overhead is closer than the sky at the horizon and it adjusts the size of the moon's image accordingly. When the moon is near the horizon, your brain miscalculates the moon's true distance and size, making it seem larger in relation to its surroundings.

One way to explore this illusion is with afterimages. These occur when certain light-sensing cones in your eyes become fatigued after staring at a bright—or brightly colored—object. You can manipulate afterimages to mimic your perception of the moon at different places in the sky. Although the actual size of a specific afterimage on your retina doesn't change, its perceived size can, depending on your perception of how far away the surface on which you view it seems to be. This phenomenon is known as Emmert's law.

Materials
A sheet of blue construction paper (A blue pen or pencil can be used instead, but the colored paper is best.)
Scissors
Glue or tape
A sheet of yellow construction paper (A white sheet of paper can be used instead, but is less preferable.)
A timer or a clock that shows seconds
A helper
An area with a clear view of the horizon and the zenith (the region of the sky directly overhead) (This part of the activity should be done mid-morning or mid-afternoon—to avoid looking at the sun—and on a day that is fairly cloudless with a lot of blue sky.)

Preparation
Cut a square out of the blue construction paper sheet, about one to two inches on each side.
Lay the yellow sheet of construction paper down in the landscape position (long-ways horizontal). Fold the paper in half (taking the right side of the paper and folding it over the left side). Then unfold the paper.
Using glue or tape, attach the blue square to the yellow sheet of construction paper, in the middle of either the left or right half of the yellow sheet. Be careful not to cover the top of the square or yellow sheet with the tape or glue.
If you do not have construction paper, you may draw a solid blue square on either the right or left side of a plain white sheet of paper, as described.

Procedure
You can complete the first part of this activity inside: Hold the yellow paper with the blue square in front of you. Stare at the blue square for 30 seconds. (Use a timer with a buzzer or have a helper watch a clock for you.) Without changing the distance between your head and the yellow paper, switch from looking at the blue square to looking at the empty half of the yellow paper. Do you see the afterimage of the square? If you cannot clearly see an afterimage, try repeating this step until you can.
Once the afterimage fades, keep your head the same distance from the paper as it was before and again stare at the blue square for 30 seconds. Then look for the afterimage on the empty half of the yellow paper. But this time try moving your head away from or closer to the yellow paper. How does the size of the afterimage change as you change the distance between your head and the yellow sheet? If you could not clearly see a change, try repeating this step until you can.
Overall, how did the size of the afterimage change as you changed the distance between your head and the yellow paper?
Next, go outside to an area with a clear view of the horizon and zenith. Do not do this at noon, when the sun is directly overhead or at twilight when the sun is low on the horizon, because this interferes with your observation of the afterimage at the zenith (the sky directly overhead) or the horizon. Mid-morning or mid-afternoon is probably the best time to do this, and the day should be fairly cloudless with a lot of blue sky to look at. Remember: when choosing the section of the sky to use, be sure that it does not coincide with where the sun is—you should never  look directly into the sun.
Stare at the blue square on the yellow sheet for 30 seconds and then look at the horizon. Is there an apparent change in the size of the afterimage? In other words, does the afterimage look smaller, larger or the same size as the blue square? You can repeat this step a few times if you are unsure of your observations.
Next stare at the blue square for 30 seconds and then look at the zenith. Is there an apparent change in the size of the afterimage? Does the afterimage look smaller, larger or the same size as the blue square? Again, you can repeat this step if you are unsure of your observations.
Overall, did the afterimage appear smaller, larger or the same size at the horizon compared with its appearance at the zenith?
Extra: Try the first part of this activity again (before you go outside), but this time try to quantify how the size of the afterimage changes depending on the distance between your head and the yellow sheet. (Be sure to always stare at the blue square from the same distance.) You could put the yellow sheet on a wall next to a ruler to estimate the size of the afterimage. Alternatively you could draw several different size squares (some bigger and some smaller than the blue square) nested together on the yellow sheet and try to see in which square the afterimage fits best. How does the distance between your head and the afterimage quantitatively correlate to the afterimage size?
Extra: Try to estimate the change in the size of the afterimage at the zenith compared with the horizon. To do this you could cut out several squares (a white sheet of paper would work), some smaller and some larger than the blue square, and hold them out at arm's length when looking at the afterimages. Try to find the squares that are most similar in size to the afterimages. Based on your findings, what is roughly the magnitude of the change of the full moon's apparent size between the horizon and the zenith?
Extra: Try to estimate the change in the size of the afterimage at 45 degrees above the horizon; that is, halfway between the horizon and the zenith. (Be sure to avoid the part of the sky with the sun.) What is the relative size of the afterimage at 45 degrees above the horizon, and how does it compare with the afterimage's sizes at the zenith and the horizon?

Observations and results
When you stared at the blue square, and then looked at the yellow sheet and moved your head away from or closer to the sheet, did the size of the afterimage increase with distance? Did the afterimage look bigger on the horizon compared with its size at the zenith?

Whereas the actual size of the afterimage on your retina doesn't change, the perceived size of the afterimage actually grows as you increase the distance between you and the surface on which you view the afterimage. (Or, in other words, the perceived afterimage size decreases as you get closer to the surface you're viewing it on.) This phenomenon is known as Emmert's law. One theory for why we perceive the full moon to be larger at the horizon compared with the zenith is that we perceive the sky overhead, at the zenith, as being closer than the sky at the horizon. In this activity this should have been apparent using afterimages; the afterimage at the horizon should have appeared larger than the afterimage at the zenith (although maybe only by a little, such as approximately 1.3 to 1.5 times larger at the horizon, depending on the exact conditions).

More to explore
Moon Illusion and Emmert’s Law (pdf), from Howard E. Gruber and William L. King, Science magazine
Solstice Moon Illusion, from NASA Science News
I See a Full Moon Rising… and Shrinking… or Do I?, from Science Buddies

This activity brought to you in partnership with Science Buddies

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