Reflections on Yad Vashem, revisited

Here's a bit of an answer to Becca's excellent question: how many mirrors do you need to achieve the effect in the Yad Vashem museum?

The answer is "surprisingly few".  Of course I don't know for sure how many mirrors and what angles the museum used, but it's possible to get a pretty stunning effect with just a handfull of mirrors -- say, one on each wall and one on the ceiling.  Let's see how this relates to what we've done in class.

The standard way of thinking about reflections is that there's a ray of light that leaves the candle, bounces off the mirror, and reaches the viewer so that "the angle of incidence equals the angle of reflection".

As always, so that we do not discriminate between right-eyed people and left-eyed people,
we have our viewer looking out of the nose.  

But for our purposes, we're going to imagine that we reflect the candle itself to the other side of the mirror.
This gives us something that looks like a standard plan view, where the mirror becomes the picture plane.

The candle to the left is real; the candle above is a reflection.
The image of the reflection is a point on the blue mirror.

 If we add one more mirror directly behind us, that means we should add another reflected candle behind the second green mirror.  We can't see that new reflection in the blue mirror, because the new reflection is behind us.

But now we reflect that reflection in the blue mirror.  And that new reflection is something we can see.  So now we get a second image of the candle.

 (Of course, the light itself doesn't go in a straight line; really the light leaves the real candle, bounces off the back mirror, then bounces off the front mirror, then reaches the viewer).

 If you keep reflecting back and forth -- first in the blue mirror, then in the green mirror, then in the blue mirror again -- you get an infinite number of reflections of the candles, meaning you get an infinite sequence of images.  (And all of this with just one candle and two mirrors!)  It looks a bit like our railroad track problems, in fact.

Notice that the images seem to converge to a point (sort of like a vanishing point) right in front of the viewer.  Does that match what Becca saw at Yad Vashem?  I'd say, yes.

 If the two mirrors aren't parallel, other interesting stuff can happen.  For example, if the two mirrors are at right angles, you'll only get two images of the candle in the blue mirror.

But if you combine the right-angle mirrors with a parallel mirror, you get lots more images.

With four mirrors, one on each wall, you seem to fill up space -- there are reflections of that one little candle everywhere you look.