Posted November 21, 2000
Last week, I played some parts of The Magic Flute and talked about how radio broadcasting works. Several people have told me that they enjoyed the bits about radio broadcasting, but not a single person had anything good to say about the opera. This is not much of a surprise, although, if there was anything less popular than opera, I would have guessed that math and physics would be it.
Another thing I noticed about last week's broadcast is that nobody said anything about my glaring factual errors. Please remember that this is the radio, not the gospel. If you want gospel, you should listen to Freya's show, which is called Dinner Music for a Pack of Hungry Cannibals. It's on at 6:00, every second Sunday, including this coming Sunday.
I'll start today's program with a sonata for piano and violin, number 454 in the Mozart catalogue. Then I'm going to play some of Mozart's well known chamber pieces, and say a thing or two about optics.
Last week I said some things about physics that nobody should ever have to hear. For example, I gave a completely misleading explanation of what refraction is. This time I'll see if I can get it right.
Refraction is the bending of a ray of light as it passes from one medium into another, from water to air for example. Normally, of course, we expect light to travel in straight lines. This expectation manifests itself in our visual cortex at such an early stage that it's impossible for us to overcome the optical illusions caused by refraction.
Two common examples of how we see refracted light, are eyeglasses and bathtubs. Eyeglasses work by bending light before it gets to your eyes; the light bends once when it passes from air into glass, and again in the opposite direction when it passes from the glass back into the air in front of your eyes. The refocusing effect of the eyeglasses is caused by a small difference between the two angles of refraction. Thick glasses can give you a bigger difference between the two angles, so they have a more dramatic effect. Incidentally, there is something called a Fresnel lens, which is a concentric series of thin ring-shaped lenses. Each ring is shaped like the thin outer edge of a regular thick lens. A Fresnel lens can achieve a similar effect to a very thick regular lens, without requiring so many pounds of glass. The optical quality is worse than a regular lens because in that you can see the lines between adjacent rings. This makes it unsuitable for eyeglasses and telescopes, but it's just right for those overhead projectors that our high school teachers like to use. Remember those concentric rings that show up on the overhead screen? Now you know.
For a second example of refraction, consider what you see when you put your finger under water and look at it from above at a 30 degree angle. Your finger looks smaller that it did when it was above water. This is because the light leaves your fingertip at a steep angle, but at the surface it refracts, and continues at a more gentle slope. When the light reaches your eye, your visual cortex interprets it as if it had been travelling in a straight line ever since it left your fingertip. This imaginary light path intersects with your finger 1/2 an inch below the surface; whereas the real light path originated 1 full inch below the surface.
Here's an exercise you can try at home without your parents' supervision. Fill an opaque white mug half way with tap water, so that the height above water and the height below water look equal. Pour the water out of the mug into a big bowl. Now fill the mug half way again, with some more tap water. Pour that first batch of water from the bowl back into the mug. Now get a towel, and mop up the water. The moral of the story? If a mug looks half full, it's more than half full. In other words, you should be more optimistic. And always have a towel handy.
I mentioned refraction last week in the context of radio waves in the ionosphere. Radio waves are simply low frequency light waves, and they refract when they pass from warm areas to cold areas in the ionosphere. Or perhaps they refract when they pass from positively charged areas to negatively charged areas. Or perhaps both. If you can answer that question, call me in the studio at 352-3706. If you want to hear the question again, we're rebroadcasting this show at 9:00 on Friday morning. That's immediately following the Sad Monster Show, which is on all night, every night.