13 December 2006

Holiday Optics

[Written in 2006]

J-Fav is on the road with Toby tonight, leaving me to my idle devices. Bad! This gives me too much of a chance to procrastinate (i.e. think about optics) while my subconscious figures out what holiday presents to purchase.

See, it goes like this.

Every other night, I take Toby on a stroll up and down picturesque Mass. Ave. here in Arlington:

We pass many storefronts with Christmas lights in them. They make pretty reflections between the panes of glass - at least, that what I think they're doing:

You can make out at least four images of "copycat" bulbs for each "initial" bulb. Not only that, if you look closely, there are little microbulbs within each copycat. What's up with this? Let's start with the copycat bulbs.

The initial image of the bulb.

This is the situation, as seen looking down from the sky. The lightbulb, A, is illuminating its surroundings; you're the observer at the bottom. If you draw at least 2 rays leaving the bulb, your eyes (wherever they are) perceive the bulb where those rays intersect. As you'd expect, the bulb looks like it's where it is! (Actually, as you probably guessed, that's slightly inaccurate, but I'll bore you with that later.)

You've noticed that although glass looks clear, a fraction of light striking it bounces off like a mirror. What happens when some of the bulb light reflects off the far window pane?

Light striking the distant pane bounces off toward your eyes at a different angle. If we follow two rays again -- the solid blue one and the dotted blue one -- you see that they exit the near pane as if they were originating from a phantom bulb, B.

So how do you get the other phantom bulbs? It seems like they're created by multiple bounces between the insides of the two panes of glass! Check it out:

The green lines show you where the several-bounce rays are ejected from the near pane. Tracing those back for both eyes shows you where phantom bulb C looks like it's coming from.

Yes, this is an opportunity to hear myself talk, but at least now I can stop wondering if the images are due to bounces amongst the panes of glass or within the panes of glass (which is where the microbulb images are probably from).

The inaccuracy I admitted to above is that these diagrams neglect the fact that light changes direction a little bit upon entering and exiting each pane of glass. The true case for the original bulb A is really more like this, just as the water in a fishtank makes your fishies look like they're someplace else:

Zoom in on this image; the pink lines more faithfully represent where the light's really going. The bulb looks like it's at A', not A.

Still awake? Guess it's time for me to figure out my holiday shopping. This is what I see above my computer screen, over in the living room:


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