MadSci Network: Physics
Query:

Re: how many repetitions can a double mirror produce?

Date: Sat Jan 6 07:09:44 2007
Posted By: Tom Hancewicz, Staff, Advanced Imaging and Measurement, Unilever Research & Development
Area of science: Physics
ID: 1167356554.Ph
Message:

I am not going to hazard a guess at the form of an equation to solve this 
problem although no doubt one could be devised. What I will give are some 
thoughts on what would be involved in considering a solution.

Theoretically, two mirrors facing each other at 0 degrees angle (parallel) 
will produce an infinite number of virtual images of an object placed 
between the mirrors. This assumes 100% efficient mirrors (no loss on 
reflection or absorption) and no attenuation of the light by the object 
whos image is being reflected. This means there will be no attenuation of 
the image intensity no matter how many reflections. The number of photon 
should remain constance under these ideal conditions. The image does get 
smaller however as you suggest because each succesive image is a virtual 
image of the previous one so the it appears as if it is being seen at the 
distance described by the total number of reflections of the image. 
Clearly this does imply that there will be a time delay upon reflection. 
This can easily be calcualted using the speed of light in the medium (you 
can make it easy by assuming the mirrors are in a chamber under complete 
vacuum). Then the time delay is simply the total distance travelled 
divided by the velocity of light in a vaccum.

Time delay = (distance between mirrors * number of reflections)/ speed of 
light

Since the speed of light is approximately 670,616,629.384 miles per hour, 
or about one foot per 1,000,000,000 seconds, if the distance between 
mirrors is 2 feet, at reflection 1 billion the time delay will be 
approximately 2 seconds. This however does not take into account the small 
delay caused by the thickness of the mirror material (presumably glass). 

However, this is all a theroetical argument. Even under the most favorable 
conditions there is no way to optically measure the experiment without 
interfereing with the result.  Any method of observing the images in the 
mirrors will attentuate the reflection. Additionally there is no such 
thing as a 100% efficient mirror or an optically flat mirror, and we have 
two mirrors. There is no such thing a perfectly parallel flawless mirrors.

In practical terms there are too many assumptions that have to be made in 
order to solve the problem in a realistic manner.


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