MadSci Network: Physics |
This is an interesting question, and requires that we make some assumptions in order to answer it. First, the assumptions: 1. The mirrors are pretty flat, but not perfectly flat. 2. The mirrors are not particularly close together -- maybe a couple of cm separation -- and a really big -- several meters in transverse dimension. 3. The person doing the viewing is looking at him or her self (I'll use the masculine in what follows just to simplify verbage) 4. The person is illuminated by a white light incoherent source (not a laser) from a long way away... say, the sun. 5. A one-way mirror is a partial reflector for all wavelengths of light with equal reflectivity of something like 50% R at all wavelengths. Under these assumptions, the observer looking at himself would see a fuzzy image that had its clearest portion when the observer is looking directly at his own eyes and which gets fuzzier as he looks further away from his eyes. The reasons for this are the following: 1. When the observer looks directly at his own eyes, he's seeing light which has reflected from his eyes perpendicularly to the mirror pair surfaces and which -- even after multiple reflections -- comes directly back at him. Each of the multiple reflections is in exactly the same direction so that there is no blurring and no ghost images are observed. But this is only when the observer looks directly at the mirror pair. 2. When the observer looks at a part of his body away from his eyes, the light which reaches his eyes must come from a point off the perpendicular line from his eyes to the mirror. The rays which are directly reflected off the one-way mirror will form a sharp but relatively dim image. For the rays which go through the one-way mirror, the situation is a little different. In this case, rays which bounce once form another image which is displaced from the first image and blurred out (because the further you are from the perpendicular, the larger the transverse displacement of the central ray from the perpendicular). The net result of all this is like what you see when you're driving at night wearing sunglasses and looking at oncoming headlights. The sunglasses don't have the reflectivity of the case of interest, but each surface acts as a mirror of about 4% reflectivity. What you see when you look at a headlight is a bright spot with a kind of blurry comet trail going away from the center of your line of sight. In this case, the bright spot is the directly transmitted light and the comet trail is comprised of the multiple reflections. The attenuation of the trail comes from the fact that the surfaces are not very reflective, so that the intensity of subsequent bounces diminishes quite rapidly. It's not exactly the same effect, but it's close... and the physics is pretty much the same. Note: Don't try this when you're driving, or you're likely to either (1) not see enough through the sunglasses while you're driving to be safe, or (2) get so disoriented by the light tails that you can't drive safely: get somebody else to drive while you do the experiment!
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