(30 minutes or less)
Remove the box lid. At the center of one end-panel of the shoe box, cut a hole large enough for one-eyed viewing (approximately 1/2 inch [1.3 cm] diameter). Then cut out a window, approximately 3 x 5 inches (8 x 13 cm), with the viewing hole in the center. Replace the cardboard in the window from which it was cut, and tape it in place along its bottom edge to form a hinge inside the box (see diagram).
At the other end of the box, make a hole for each straw approximately 1/2 inch (1.3 cm) to each side of the center of the panel.
Cut the piece of posterboard so that it is the same height as the box and about 2 inches (5 cm) wider than the box. Fold back 1 inch (2.5 cm) on each side to make two flaps. Make two holes in the main portion that coincide exactly with the two holes in the end of the box. Tape or glue the flaps to the inside sides of the box, using them as spacers to position this piece 1 inch (2.5 cm) from the end with the holes (see diagram).
Insert the straws into the holes. The double set of holes will keep the straws properly aligned.
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. Use clay to mount the circles on the ends of the straws inside the box.
(15 minutes or more)
With the cover on the box and the hinged window closed, close one eye and look through the viewing hole at the 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 is very difficult to judge which circle is closest to you.
Fold the window down 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 that 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. You may notice that it is 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-color 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 be easily distinguished.
Large, distant objects can appear to be 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 of the circles really is. Since they are not actually the same size, this means that, for the smaller one to look the same size as the larger one, it will have 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.
There is a pattern on the pupa of the butterfly Spalgis epius 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.