A Physics Riddle (5/3/2010)

This was originally posted on a horrible site called Myspace. When Myspace underwent a redesign in Fall 2010, hundreds of insightful reader comments that had been left over the years were lost. I have since deleted my account there.

Your assignment is to design a simple system in which a laser beam can be made brighter — i.e., its intensity increases — by having the beam pass through a particular “mystery object,” as opposed to the beam not passing through that object. You may not use any additional power (the object must be entirely passive), you may not change the beam's diameter or wavelength, and the beam must remain in a straight line from beginning to end.

This is not a trick question -- the solution can be easily demonstrated in a tabletop setup. Without the mystery object, it’s a dark beam; hold the object so that the beam is passing through it, and it’s a bright beam.

Hint #1: In preparing the system, you will be doing something to make the laser beam less intense. Adding in the mystery object will then remove this effect to some degree, making the beam brighter again.

Hint #2: If you put the mystery object in front of a standard, unprepared laser beam, the beam will actually get darker! But putting it in the prepared beam makes it brighter. Yeah, it really does.

The solution is below...scroll down to read.

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The secret ingredient is polarization. It turns out that if we orient a laser beam so that it is polarized (for example) vertically, we cannot re-polarize it horizontally merely by then passing it through a horizontally oriented polarizing filter. Doing so cuts out almost the entire beam, because there is virtually no horizontal component of vertically polarized light. However, we can rotate the polarization of a beam of light by 90° if we do it in two stages of 45° each. Doing so cuts out about half of the light -- but half is more than almost nothing. So...

Set up a laser pointer so that the beam is polarized vertically.* Then put a horizontally oriented polarizing filter in front of it. (3-D movie glasses consist of two such filters, each oriented differently.) This will reduce the beam to almost nothing. Now here comes the magic trick: Place another polarizing filter oriented at 45° between the laser and the horizontal polarizer. The beam will become much brighter with the 45° filter in place than with the filter out.

This is counterintuitive, because when viewed in ambient, non-polarized light, the polarizing filter (at any orientation) appears dark, like a tinted window. You wouldn't think that a "darkening" filter could make a laser beam brighter, right? But in this case, it does. Magic.

One clever way to solve this would be to realize that it's patently impossible to take an ordinary laser beam and amplify it using a passive device. (If we could do that, we'd have an unlimited source of energy, like a perpetual-motion machine.) So, the laser beam must have to be prepared in some special way -- one in which the "extra" light has already been produced; it's just been made temporarily unavailable. The problem then becomes simpler: how to "hide" light such that it can be revealed by bringing in something else. But if you start by assuming that the passive device must somehow generate energy out of nothing, you'll never solve this problem. You may also be tempted to assume that the passive device has to be the last thing in the optical chain, when there's nothing in the riddle that says that it has to be. So, the riddle is a good illustration of how we unwittingly apply assumptions all the time -- assumptions that can paralyze our ability to solve a particular problem.


* Both laser pointers that I tried emitted polarized light. If you happen to have a laser that emits a non-polarized beam -- i.e., the polarizing filter cuts out 50% of the light at all orientations -- you'll have to add a third filter (in this case, one oriented vertically) immediately in front of the laser. The "trick" should still work.