MadSci Network: Physics
Query:

Re: What would one see in two closely spaced, opposing mirrors?

Date: Fri Aug 18 04:58:34 2000
Posted By: Steve Guch, Post-doc/Fellow, Physics (Electro-Optics/Lasers), Litton Systems, Inc., Laser Systems Division
Area of science: Physics
ID: 964891776.Ph
Message:

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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