In today’s classic column, Cecil addresses the issue of why “objects in mirror are closer than they appear”. An interesting point is that, in a sense, they’re also farther than they appear. If you gauge the distance soley by the apparent size of the image, then everything that Cecil said was correct. However, if you define the distance to the image in terms of parallax, as is generally done in discussions of optical physics, then you find that the image is only a few centimeters on the other side of the mirror, and hence the objects are much farther.
I’m not sure I follow your meaning here, Chronos. I understand how parallax is used to determine distances to some astronomical objects, but I’m unclear how this relates to objects seen in passenger-side mirrors.
Parallax is the basis of binocular depth perception. Your brain compares the images from your two eyes, knows how far apart they are, and calculates the angles to give an estimate of distance.
Shorter distances require the eyes to turn in more to allow both to focus on the same thing. Since the convex mirror changes the angles, distant objects that would have a very small parallax angle would seem to have a much larger one. Your two eyes would have to turn in more, no matter how far away the object is.
Since most of our distance estimates are based on size, this would only come into play if you were looking at something for which you didn’t know its size. So, for objects with out a size reference, parallax would make them seem close, rather than far away.
The way I worked this out is to draw a ray diagram. draw two rays from one point, representing your object. Extend them out to meet a pair of eyes a distance apart. Then, add in a convex mirror in the middle space. Draw the way the rays would reflect off them, and extend them until they are about the same distance apart. Note that the rays reflected off the mirror are a lot shorter than the ones that extended without it. Now, extend the reflected rays through the mirror until they cross. This distance should be shorter than the distance from the mirror to the actual object, but this is the parallax-derived distance your eyes and brain come up with.
I’ll bet I just made it worse with that last paragraph. Can anyone else explain it better?
Not better. That was excellent. Maybe simpler.
Hold your thumb out in front of your face and look at it. Close one eye at a time, alternating rapidly. The apparent difference is parallax.
Geeeez, never mind. I just wrote what I posted. Delete it/erase it/ send it away/. I promise to read the full and complete posting list in the future before I show my ass again.
Hmm, perhaps I can clarify. In the lab I taught last year, one of the experiments involved measuring the distance to the image in flat and convex mirrors. You can’t just poke a ruler through the mirror to where the image is, but what you can do is put another real object in the same place, and then measure the distance from the mirror to the object representing the image. We used vertical dowells which protrude above the height of the mirror. The way that you can tell that the second dowell is in the same place as the image is that when you look at it from different angles, the top of the dowell is always contiguous with the image of the dowell in the mirror-- It looks like one unbroken dowell. Those different angles can just be the angles to a person’s two eyeballs, but it’s easier to see if you move around a bit too. This is the parallax definition of the distance to the image, and it’s what I was referring to in the OP.
BTW, tcburnett, what was so horribly wrong with your explanation of parallax?