[Physics] Are infinite reflections between two mirrors really infinite

opticsreflection

As written in the title it's a somewhat rhetoric question, so let me be more clear.

Let's say I have two mirrors facing each other. They are perfectly aligned and perfectly reflective. I'm looking through one of them (using the one-sided mirror effect) and see what seems to be infinite reflections.

If I look closely at the vanishing point, I obviously can't see very well what goes on there, because the reflections are too small. My question is, are there other limitations?

a) If I look close enough to the vanishing point, is there a point at which the light would have to travel too much distance to reach me that no photon would actually make it?

b) If I start looking immediately after turning on the light, it should take a tiny amount of time until all the reflections are created, i.e., it takes time for light to do all the back and forth trips it takes to create the very small images. How good a microscope (telescope?) would I need to be able to see the image being created? That is, to look at a spot and see nothing, and then some epsilon of time later see an image appear.

Infinite reflections

Best Answer

You will only ever see a finite number of images, for practical reasons.

  1. No mirror is perfectly reflecting. Some small fraction of light is always absorbed each time light is reflected. As you can see from your photo, the images get darker, and by the 8th image they are too dark to distinguish. This is caused by light losing energy due to the bounces between the mirrors. Light takes about 3ns to travel 1m, so if the mirrors are 2m apart it take approx 0.1 micro-seconds (one ten-millionth of a second) for the light from the 8th image to reach you. The delay between the first and last image is too small for you to notice.

  2. Even with mirrors which are perfectly reflecting, the images get smaller. At some stage they are too small for your eyes to resolve clearly. But even allowing for a telescope which can resolve images perfectly, at some stage they will be not much bigger than either the wavelength of light or the atoms in the mirror. At this scale the reflections are too fuzzy to distinguish, and they merge into each other.

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