Reflections of You

First, why do you see images in a mirror at all? The fact that you do see images is so familiar from an early age that you've probably not thought about it, unless in school. The reason why it's not obvious is that light from a real object is streaming off in all directions, bouncing off all points on the mirror in all new directions.

After all, if you look at an object directly, you see it where it is because light travels in straight lines, and the only relevant light from the object is that flowing from the object directly to your eye. If you look in a mirror, why do you see the the object at just one place?

As we will see, the reason is geometry, and the fact that reflection occurs at the same angle, incoming and outgoing.

The simulation shows a plane mirror viewed on edge, a few light emitting objects, and that traditional disembodied eye that's in all these sort of optics diagrams. Imaging Plane Reflector Click on an object to activate it: this will cause a light beam to be shown in one direction. Click and drag on the beam to see what happens with light in different directions. Try to reflect the light into the eye: if you succeed, the eye "sees" the object, and the virtual image of the object is shown where the eye sees it. (The image is, of course, on the straight line the light enters the eye, since that's what your perception does for ordinary direct vision of objects.) All the other light beam directions from the mirror don't enter the eye and so aren't seen in the mirror. (by this eye, anyway...you can move the eye by clicking at the left)

After you've made the eye see one object, leave its beam entering the eye and click on another object to activate it. After you've made the eye see all the objects, you can see the set of virtual images behind the mirror are just like the objects themselves in front of the mirror, in the same order.

Jabberwocky Wait a minute, what about Alice's comment on the previous page, that mirrors reverse left to right? Well, if in front of a mirror you hold up a piece of transparent plastic with words written normally on it, and look thru the plastic at the image, you'll see the image letters also read normally. But if you turn the plastic around so you see the words backwards, they're backwards in the mirror image also. Alice held up a (non-transparent) book to the looking-glass, so her situation was the second case, like reading text from the back side of the (transparent) page. Go try it.

Hmmmm. Tricky.

But we were going to talk about corner reflectors reversing images, at least relative to ordinary flat mirrors. So here's the same situation as the above simulation but with a corner reflector. Imaging Corner Reflector If you click and drag and make the eye see the objects in the mirror, you'll notice that the order of the virtual images is just the reverse of the real objects, and so the reverse of the plane mirror case above. This isn't exactly new, but there's a patent on it anyway. An artist's perspective: can you really look yourself in the face in a mirror?

Historical Note
The ancient Greeks worked out a lot of the optics of reflections, since it's so close to geometry, at which they excelled. (curved mirrors are non-trivial math) Euclid not only wrote his famous geometry book, he wrote an Optics as well. The basic rule that the angle of incidence is equal to the angle of reflection, from which so much follows, was simply a postulate, like a geometric postulate. We just taken it as given and we derive results like the simulations on these pages. A little later the brilliant Archimedes, who did a lot more than shout Eureka, like inventing large mirrors to set afire the Roman ships besieging his city, thought of an elegant argument why the rule should be true.

Archimedes's idea is really quite modern physics, being based on symmetry. He noted that if you reverse the direction of the light beam nothing changes! If you think about it, you can see that accepting this as a principle allows you to prove that the angle of incidence equals the angle of reflection, since the two angles are just interchanged by reversal.

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