How does the angle between two adjacent mirrors affect the number of images formed?

Answer 1

The number of images formed will largely depend on perspective. The visual stimuli around it may also colour what we, as humans, would perceive as recurring images. As a result it is difficult to answer your question exactly. It is however possible to answer what the maximum number of times a light particle could reflect between each mirror.

In the case of them being exactly adjacent and the angle between them less than 90, the number will always be infinity. If looking in to the two you should see the mirrors curve around as light at the furthest points has further to travel after a reflection. As a result tt may not appear infinite but this is because the mirrors quickly contract in size the further in you look to the point it becomes to small to see by the human eye. This may not be helped by the surrounding visual stimuli.

If there is even a millimetre gap however it is possible to put a number on it given some assumptions.

I did manage to write an algorithm to calculate it however it was both recursive and complicated, especially without the use of pictures. I have drawn out the assumptions which need to be made in case anyone more mathematically minded wants to try and find a more elegant solution.

Assumptions

We will assume the light powering the reflections is infinitely powerful.

The mirrors are perfectly smooth and always reflects light at precisely the same angle it hit.

For the purposes of simplicity we can assume the mirrors are the same length. If they were of different length it would be sufficient to simply take the shortest.

We will only consider light from one source. While unrealistic we will assume the light is uniformly coming from a single direction pointing perpendicular towards where the mirrors would intersect.

Formula

Let x be the maximum number of reflections.

There are three factors which determine the number of reflections of light.

1. The angle of the mirrors.

2. The length of the mirrors.

3. The distance between the mirrors.

Let the angle between the mirrors in degrees be a.

Let the length of the mirrors be w.

Let the distance between the mirrors at their closest point be d.