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Size and Distance

Science Snack
Size and Distance
So close, yet so far away.
Size and Distance
So close, yet so far away.

By removing clues to the actual size and distance of an object, you can trick your brain into thinking that two similar objects of different sizes are really the same size. You can then compare what you see with limited information to what you see when you have complete information.

Tools and Materials
  • Shoebox with lid
  • Knife or scissors
  • Tape
  • Two drinking straws
  • A piece of poster board or similar-weight cardboard, a little larger than the end of the box
  • Two coins of different sizes (for instance, a quarter and a dime)
  • Construction paper that contrasts with the inside color of the shoebox
  • Modeling clay or reusable adhesive putty
  1. Remove the box lid.
  2. At the center of one end-panel of the shoebox, cut a 1/2-inch square or round viewing hole, large enough for one eye to look through.
  3. Then cut out a window, approximately 3 × 5 inches (8 × 13 cm), with the viewing hole in the center.
  4. Replace the cardboard window and tape it in place along the bottom edge to form a hinge inside the box (click to enlarge diagram below).
  5. At the other end of the box, make a hole for each straw, approximately 1/2 inch (1.25 cm) to either side of the center of the panel.
  6. Cut the piece of poster board so it’s the same height as the box and about 2 inches (5 cm) wider than the box.
  7. Fold back 1 inch (2.5 cm) on each side of the poster board panel to make two flaps. Then make two holes in the posterboard that align exactly with the two holes in the end of the box.
  8. Position the two posterboard flaps inside the box about 1 inch (2.5 cm) from the end with the two holes (see diagram below). Tape or glue the flaps to the inside sides of the box.
  9. Insert the straws into both sets of holes. The double set of holes will keep the straws properly aligned.
  10. Using the quarter and dime as templates, cut one circle of each size from the construction paper. Make sure the color of the construction paper contrasts strongly with the color of the inside of the box.
  11. Use clay to mount the circles to the ends of the straws inside the box.
To Do and Notice

Put the cover on the box and close the hinged window. Move the straws so that the locations of the circles is unknown. Close one eye and look into the viewing hole with the other eye. 

With your other eye, look through the viewing hole at the construction paper circles. Lift the end of the box cover closest to you and slide it away from you until adequate viewing light reaches the inside of the box. Push or pull on the straws from the outside rear of the box until the mounted circles appear to be the same size. Note that your depth perception is almost nonexistent: both circles look essentially the same distance away, and it’s very difficult to judge which circle is closest to you.

Fold down the viewing window and look with both eyes to see the actual positions of the circles. (You may have to move your head back a little from the box to get both circles focused.) Note that depth perception is now a factor and the circles no longer look the same size or the same distance away.

Position the small disk a couple of inches closer to you than the large disk. With both eyes open, look through the window at the disks. Notice that you have no trouble establishing their size and distance.

Now close one eye and notice that it may be much more difficult to tell whether the small disk is now actually a small disk that’s close to you, or a large disk that’s far away. You can also use the dime and quarter by themselves, without building the box, to illustrate the same principle. Close one eye. Holding one coin in each hand, move them toward or away from your viewing eye until they appear to be the same size. A solid-colored background gives less distraction than an irregular background. A very bright, solid-colored background works best, so that the coins appear essentially in silhouette, and their features cannot easily be distinguished.

What’s Going On?

Large, distant objects can appear the same size as small, nearby objects. Under normal viewing conditions, with both eyes open, you have the ability to perceive depth. If two objects appear to be the same size, but you know that one is farther away than the other, your brain tells you that the distant object is larger.

When one eye is closed, your depth perception is impaired. In the case of the circles, you can’t tell how far away either really is. They are not actually the same size, so in order for the smaller one to look the same size as the larger one, it has to be closer to you than the larger one.

With both eyes open, you can gather more information and more points of view, and so you can make more accurate judgments about an object’s size, shape, and distance from you.

Going Further

There is a pattern on the pupa of the Spalgis epius butterfly that looks like the face of a rhesus macaque monkey. Even though the pupa is only half as wide as a human fingernail, it still seems to scare away predatory birds who mistake it for a more distant, and therefore larger, monkey.

The sizes and distances of the sun and the moon are such that total solar eclipses can be viewed from earth. Although the sun is much larger than the moon, it is also much further away, and the angular diameters of these two celestial objects are almost the same, which allows the moon to block out the sun almost perfectly during a total solar eclipse.