Today’s Wonder of the Day was inspired by ILoveWondering. ILoveWondering Wonders, “Why does the moon appear so small?” Thanks for WONDERing with us, ILoveWondering!
If you're looking for the Arch as you're approaching St. Louis on the highway, you can see it from several miles away. When you first catch a glimpse of it, you might be surprised that it's so small. As you get closer, however, it appears larger.
What's going on here? The Arch itself obviously doesn't change in size. Depending upon how far away you are when you view it, however, it can appear to be very large or very small. Why exactly do objects appear to be smaller the farther away we are from them?
The answer lies in the concept of perspective and the difference between apparent size and actual size. These phenomena exist because of the optics of our eyes and how they process the rays of light that reflect off of objects so that we can see them.
For example, the actual size of the Arch doesn't change. It can be measured in meters or feet. Its apparent size, however — what we perceive its size to be — depends upon an angle, which can be measured in degrees.
The visual angle that determines apparent size can be thought of as the angle at the top of a triangle. The eye is the top of the triangle, and the bottom of the triangle is formed by the ends of the object you're looking at.
Another way to think of the visual angle is to think of your field of vision as looking out through a traffic cone. If you hold the top of the cone to your eye, your field of vision is limited by the ends of the bottom of the cone. An item at the bottom of the cone (farther away) will take up less of your field of vision and appear smaller. An item at the top of the cone (close to your eye) will take up much more of your field of vision and thus appear larger.
Mathematicians call the relationship between apparent height and distance an inversely proportional relationship. An equation might look something like this: apparent height = actual height / distance. As distance increases (object gets farther away), apparent height decreases (object appears smaller).
You may have noticed this phenomenon in another context. Have you ever looked closely at the rearview mirror of an automobile? There's a good chance it probably has a warning printed on it that reads something like "objects in mirror may be closer than they appear."
When a driver looks at the rearview mirror on the passenger side and sees a car, that car appears to be farther away (and smaller) than it really is. This occurs because the mirror is convex (curved such that the middle bulges outward slightly).
Convex mirrors are used on cars, because they distort images in such a way that everything gets compressed. This allows drivers to enjoy a wider field of view. Even though some of the images may be closer than they appear, at least drivers can see more rather than less! For safety reasons, a smaller blind spot takes precedence over more accurate distance perception.