MadSci Network: Physics |
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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