March 27, 2008

Objects In Mirror Closer Than They Appear

Stupid Question ™
Sept. 23, 1999
By John Ruch
© 1999

Q: Why are objects in a car mirror closer than they appear?

A: Mirrors that carry the familiar warning, “Objects in mirror are closer than they appear” are not regular flat mirrors. They are slightly convex, meaning they bulge outward like the side of a ball.

Convex mirrors are useful because their large surface area allows them to reflect light from a much bigger area than a flat mirror of the same size. You’ve probably seen large, round convex mirrors in convenience stores, where they’re used to observe the entire store from one point.

According to General Motors spokesperson Terry Rhadigan, convex mirrors are now ubiquitous on the passenger side of cars because they help eliminate blind spots.

Flat mirrors are fine for the driver’s side and rear-view, because they’re close enough that the driver can adjust his or her head to see a wide range of angles. But the passenger-side mirror is far away, and, if flat, would offer only a very limited field of vision. Making it convex gives you a field of vision about 30 percent bigger, so changing lanes is much safer.

However, the convex mirror also creates what Ohio State University physics professor Linn Van Woerkom calls “a classic geometric optics problem”: this useful wide-angle reflection also results in a distorted image.

In a flat mirror, light rays bounce off at regular 90-degree angles, producing a near-perfect duplicate of the reflected object. The reflected object will look as big as in real life, and as far “in” in the mirror as it is away from the mirror.

But convex mirrors gather light rays around the curved surface and reflect them at varying angles. One result is that the image is compressed around the most bulging part, and stretched out near the mirror’s edges.

This compression occurs in such a way that the image can never be as large as (or larger than) the object that’s being reflected. A car, for example, seen in a convex mirror will look smaller than it really is.

When we’re very young, we learn through experience that when a familiar object looks relatively smaller, it is usually farther away—even in flat mirrors. The smaller it looks, the farther away it is (and vice versa).

Since convex mirrors shrink images, they can fool us. If you’re not used to a convex car mirror (which is so slightly convex it looks flat), you may think the slowpoke car you want to pass is farther away than it really is, cut somebody off, and cause a wreck.

Hence, the warning that objects in the mirror are closer than they appear.
Or hence the warning in the US, anyway. A Ford spokesperson tells me that many cars in Europe use convex mirrors on both sides of the car for extra safety, and none of them carry the warning at all.

Perhaps the product-liability warning is just a reflection on our litigious society.

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