Take a wine glass, filled with white wine if you like, or water if it’s too early in the day or you don’t drink wine. Shine a bright light from one side (in the pictures here it’s an LED torch; you can see the reflection of its multiple elements near the bottom left). Now look at your fingerprints on the opposite side of the glass. If you hold the glass firmly, they show up clearly. When you loosen your grip slightly, the image of the fingerprints becomes weaker, as the progression of images from left to right shows.
What’s going on? When the light hits the far outside wall of the glass (the side that your finger is touching) it is completely reflected if it strikes above a certain angle (called the critical angle). All of it comes back. The glass acts like a mirror at these angles in a phenomenon called total internal reflection. So you shouldn’t be able to see anything on the other side of the mirror.
But a closer look at Maxwell’s equations for the behaviour of light reveals an interesting subtlety. The reflected light doesn’t just come straight back. Some of it takes a little peek above the surface, as it were, like a seal sticking its head above the water for a quick look around before it dives back underneath. This part of the light is called an evanescent wave. It hardly goes out any distance at all, but if there is something in the way that can affect it (like the tops of the fingerprint folds in your fingers), then it will notice. In this case, that part of the light gets scattered, and shows up the bits (and only the bits) that are touching the glass.
Try it for yourself.
It’s a difficult concept to explain in words (I hope my physicist colleagues don’t laugh at my efforts too much), and much easier to understand in equations. This is how scientists think about it, but one has to admit that this way of thinking isn’t for everyone. When it works, though, it can work spectacularly well. This way of thinking, for example, made possible the development of optical fibres, which work because light bounces merrily along inside them by total internal reflection, sometimes for many kilometers, and can be picked off at any point by a process analogous to looking at your fingerprints through a wine glass. A colleague who was responsible for one of the major mathematical steps in the development process celebrated by doing a naked handstand in the corridor of the department where he worked.
He had to celebrate that way, because he didn’t drink.
But whether you do or don’t drink, enjoy Christmas. Cheers! Next post will be in the New Year.
Image: Len Fisher (free to reproduce with acknowledgment and website link).