What happens when you place two mirrors facing each other? Is it possible to have an infinite amount of reflections?


This question reminds me of Zeno's paradoxes.

It is assumed that the two mirror surfaces are absolutely parallel.

In classical physics the electromagnetic waves that create the reflections are uniform and the energy loss due to the reflection ( depending on the material of the glass) will be what will make the reflections fainter and fainter, but the process is continuous and the limit will be a limit in luminosity. In principle a totally reflecting material would have no limit, going to infinite reflections as time goes to infinity. {corrected from the original statement that the wavefronts are instantaneous: Maxwell's equations obey special relativity i.e. the velocity c of light is finite}

Reality is quantum mechanical and also special relativity dependent.

With special relativity in the problem it will take time to reach the next reflection, so even for a total reflector infinity will also be reached only at infinite time, during observation, though there will be an enormous number of reflections.

Quantum mechanically there can not be a totally reflecting mirror, even in a thought problem. There will always be a probability of absorption and thus termination of the wavefront eventually, the images getting less and less defined until they become individual photons and finally totally absorbed.

Since quantum mechanics reigns, in reality, no, there will not be an infinite amount of reflections.

  • $\begingroup$ Thank you for providing a concise answer! And for including the quantum mechanics portion. :) $\endgroup$ – Quaxton Hale Feb 27 '13 at 5:02

Such arrangements are common in lasers: "An optical cavity, resonating cavity or optical resonator is an arrangement of mirrors that forms a standing wave cavity resonator for light waves. Optical cavities are a major component of lasers". https://en.m.wikipedia.org/wiki/Optical_cavity

The loss in such resonators are characterised by the q factor: https://en.m.wikipedia.org/wiki/Q_factor

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    $\begingroup$ To fully answer the question, you need to point out that to get infinite reflections, you would need a Q factor of infinity, which is not achievable in practice. Any non-infinite Q-factor will eventually lead to the dissipation of the input energy. $\endgroup$ – Nuclear Wang Jun 24 '19 at 18:33

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