. Why do you sometimes see a circular rainbow surrounding a light?
It is most often caused by the bending of light by mist around the light or by flaws in the optical components through which you are viewing the light. Whenever light passes through a clear material, its path bends. In most cases, you only notice that the light is distorted by its passage through the material. But different colors (wavelengths) of light bend by slightly different amounts so that the colors of light sometimes appear to come from slightly different directions. That's the origin of the rainbow you see.
. Why do you think you see water on a road ahead of you when it's not really there?
On a sunny day, heat from the pavement can create a layer of very hot air at the surface of the road. Since hot air is less dense than cold air, its index of refraction is slightly less than that of cold air, too. As light from the sky enters this layer of low-index air, that light is bent. Light from the sky far out in front of you is turned upward so that you see the sky "reflected" from the road's surface (actually bent upward by the air above the road's surface). You interpret this sky light as coming from a pool of water on the road. But as you approach the road and look down at it, you see that the road is dry and black.
. Why does purple bend more in a prism than, say, red?
Purple (or violet) light travels slower in most materials than does red light. That occurs because violet light is higher in frequency than red light and gives the charged particles that it jiggles about less time to move up and down. With very little time to move, these charged particles barely notice that they are parts of atoms and molecules and respond easily to the passing electromagnetic wave. But when red light pushes and pulls on charged particles, there is more time for them to find the limits of their freedom. These charged particles are not able to move so easily when pushed on by a passing wave of red light so they do not interact with that passing wave as well as with one of violet light. Thus red light passes by with less effect and it behaves more like it would in empty space. Violet light, which interacts relatively strongly with the atoms it passes, slows down more than red light. Since red light travels more quickly than violet light, it bends less in passing through a prism. Violet light slows down more and bends more than red light.
. Why doesn't light go through the other side of a water droplet, refracting as it goes through, rather than reflecting back?
Actually, 96% of the light hitting the "other side of a water droplet" does pass out of the droplet. What you see in the rainbow is the 4% that reflects back from the far side of the water droplet. If all of the light reflected, the rainbow would be much brighter.
. Why is a blue flame hotter than a red flame?
The colors of flames can be deceiving because they involve emissions from particular atoms (which impart their own characteristic colors to the light they emit). However, a blue-hot object such as a star is hotter than a red-hot object such as a glowing coal in the fireplace.
. Why is it any worse to observe a solar eclipse rather than a normal glimpse at the sun?
The problem with looking at the sun during a solar eclipse is not that it is somehow brighter than normal but rather that (1) you tend to stare at it and (2) the size of its bright region is reduced so that it doesn't hurt as much to stare at it. It's hard to stare at the full sun because it feels uncomfortable but looking at a tiny part of the sun may not feel bad enough to make you avert your eyes. Nonetheless, that tiny part of the sun can cook your retina and cause permanent damage.
. Why is it that after swimming in a heavily chlorinated pool, you can see the spectrum around lights?
Your eye works very hard to keep all of the different wavelengths of light together so that they can form sharp images on your retina without any color errors. If you look at a white light bulb, all of the different colors from that bulb must arrive together on your retina or else you will see colors where they shouldn't be. Keeping these colors together is no small task and is one of the biggest problems encountered by lens makers for cameras and telescopes. The chlorine in a pool evidently upsets your eye's ability to control these color errors. However, I'm not sure what goes wrong or why chlorine causes this problem.
. Why isn't the sky bright blue when the sun is red?
During the day, the sky is blue because the air and dust in the air scatter mainly blue light toward your eyes. They also scatter some red light, but the blue light dominates. But at sunset, things change. The setting sun approaches the earth's atmosphere at a very shallow angle so that it must travel many kilometers through the air before reaching your eyes. During this long trip, most of the blue light is scattered away and the sun appears very red. If the path is long enough, the blue light is scattered away many kilometers to your west so that there isn't much of it left. When this occurs, even the sky around you appears somewhat reddish because there just isn't any more blue to scatter. The missing blue light is visible to people living 50 or 100 kilometers to the west as their blue sky.
. Why, if white doesn't absorb heat, do I get very hot when I wear a white shirt?
A white shirt doesn't absorb visible light (or at least very much visible light), but it may absorb lots of infrared light. Since much of the sun's light and heat are in the form of invisible infrared light, that infrared absorption can be very important. There are many materials that appear white to your eye that do absorb strongly in the infrared and thus get very hot in sunlight.
. During a total solar eclipse, does the moon make first contact with the sun on the eastern limb or the western limb? Can you explain this to me?
The moon orbits the earth from west to east. By that, I mean that if the earth were to stop turning, the moon would then rise in the west and set in the east. During a total solar eclipse, the moon is drifting directly in front of the sun. Since the moon moves from west to east, it will first block the western edge of the sun, the western limb. In contrast, during a total lunar eclipse, the moon is drifting into the earth's shadow. Since it is moving from west to east, its eastern edge will enter the shadow first.