A rainbow is truly circular, not parabolic. Passing through the exact center of that circle is the line that runs between the sun and your head. Each colored arc of the rainbow is located at a particular angle away from this line—the red arc is farther from the line than the violet arc is.
The glass in the rear view mirror is cut so that it forms a thin wedge—it’s thicker at the top than it is at the bottom. Its back surface is fully mirrored by a layer of aluminum. For daytime use, the mirror is oriented so that light from behind the car enters the glass, reflects from the layer of aluminum on the back surface, and returns through the glass to your eyes.
But when you tip the mirror upward for night use, the mirrored back surface presents you only with a view of the car’s darkened ceiling. However, there is a weak second reflection from the clear front surface of the mirror—whenever light changes speeds, as it does upon entering the glass, some of that light reflects. About 4% of the light striking the front surface of the mirror from behind the car reflects without entering the glass and is directed toward your eyes. Since the image you see is about 25 times dimmer than normal, it doesn’t blind you the way a reflection from the mirrored surface would.
Light consists of electromagnetic waves, meaning that it is composed of electric and magnetic fields. While light isn’t affected by other electric or magnetic fields, it is affected by gravitational fields. Like everything else in our universe, light falls when exposed to gravity. However, because light travels so fast, it’s very hard to detect that it falls. The first observation of light falling in a gravitational field was made during a total eclipse in 1919 and served as dramatic confirmation of the predictions of Einstein’s general theory of relativity. As for light traveling in a circle, this can occur near the surface of a black hole. When light traveling tangent to the surface of the black hole falls at just the right rate, it will orbit the black hole indefinitely.
The first step in explaining a mirage is to understand why the sky is blue, or why it has any color at all. If it weren’t for the earth’s atmosphere, the sky would be black and dotted with stars. That’s how the moon’s sky appears. But the earth’s atmosphere deflects some of the sunlight that passes through it, particularly short-wavelength light such as blue and violet, and this scattered light (Rayleigh scattering) gives the sky its bluish cast. When you look at the blue sky, you’re seeing particles of light that have been scattered away from their original paths into new paths so that they reach your eyes from all directions.
The blue light from the sky normally travels directly toward your eyes so that you see it coming from the sky. But when there is a layer of very hot air near the ground in the distance, some of the blue light from the sky in front of you bends upward toward your eyes. This light was traveling toward the ground in front of you at a very shallow angle but it didn’t hit the ground. Instead, its entry into the hot air layer bent it upward so that it arced away from the ground and toward your eyes. When you look at the ground far in front of you, you see this deflected light from the blue sky turned up at you by the air and it looks as though it has reflected from a layer of water in front of you. This bending of light that occurs when light goes from higher-density cold air to lower-density hot air is called refraction, the same effect that bends light as light enters a camera lens or a raindrop or a glass of water. Whenever light changes speeds, it can experience refraction and light speeds up in going from cold air to hot air. In this case, the light bends upward, missing the ground and eventually reaching your eyes.
Sonar stands for “sound navigation ranging” and involves the bouncing of sound waves from objects to determine where those objects are. It’s based on the reflection of sound waves from objects. Whenever a wave of any sort moves from one medium to another and experiences a change in speed (or more generally, a change in impedance), part of that wave reflects. Because sound travels much faster in solids than it does in air, some sound reflects when it moves from air to rock—which is why you hear echoes when you yell at a mountain! But even more subtle changes in the speed of sound will cause modest reflections. Thus a sophisticated sound generator and receiver can detect objects immersed in water or buried in the ground. Another form of sonar is used in medical imaging—ultrasonic imaging.
Infrared, visible, and ultraviolet light are all electromagnetic waves. However these waves differ in both their wavelengths (the distances between adjacent maximums in their electric fields) and in their frequencies (the number of electric field maximums that pass by a specific point in space each second). Infrared light has longer wavelengths and lower frequencies than visible light, while ultraviolet light has shorter wavelengths and higher frequencies than visible light. We can’t see infrared or ultraviolet lights because the cells of retinas aren’t sensitive to these lights. Nonetheless, we can often tell when those lights are present—we may feel infrared light as heat on our skins and we may find ourselves sunburned by ultraviolet light.
When a light wave enters matter, the light wave’s electric field causes charged particles in the matter to accelerate back and forth. That’s because an electric field exerts forces on charged particles. The light wave gives up some of its energy to these charged particles and is partially absorbed in the process. However, the charged particles don’t retain the light’s energy very long. They are accelerating and accelerating charged particles emit electromagnetic waves. In fact, they reemit the very same light wave that they absorbed moments earlier. Overall, the light wave is partially absorbed and then reemitted by each electrically charged particle it encounters, so that the light continues on its way as though nothing had happened.
However, something has happened—the light wave has been delayed ever so slightly. This absorption and reemission process holds the light wave back so that it travels at less than its full speed. If the charged particles in the matter are few and far between, this slowing effect is almost insignificant. But in dense materials such as glass or diamond, the light wave can be slowed substantially.
Actually, higher frequency violet light is slowed more than lower frequency red light because violet light is more effectively absorbed and reemitted by the atoms in most transparent materials. That’s because when a high frequency light wave encounters the electrons in an atom, the jiggling motion is so rapid and the electrons’ motions are so small that the electrons never reach the boundaries of the atom. As a result, those electrons are able to jiggle back and forth as though they were free electrons and they do a good job of slowing the light wave down. But when a low frequency light wave encounters the electrons in an atom, the jiggling motion is slower and the electrons’ motions are so large that they quickly reach the boundaries of the atom. As a result, those electrons aren’t able to jiggle back and forth as far as they should and they don’t slow the light wave down as well.
I would expect that certain black light sources would cause tanning with only modest burning while other black light sources would cause burning with only modest tanning. Black light—also known as ultraviolet light—consists of very energetic light particles. The particles or photons of ultraviolet light contain enough energy to break chemical bonds and rearrange molecules. When you’re exposed to such energetic light, it causes damage to molecules in your skin cells and your skin may respond by darkening in the process we call “tanning.” But ultraviolet light is a general term that covers a broad range of wavelengths and photon energies. Long wavelength/low energy ultraviolet light tends to cause tanning while short wavelength/high energy ultraviolet light tends to cause burning—it directly kills cells. But these differences aren’t sharp and any ultraviolet light will cause some amount of skin damage.
Biological tissues themselves are relatively transparent. They’re not good conductors of electricity and electric insulators are typically transparent (quartz, diamond, sapphire, salt, sugar). But we also contain some pigment molecules that are highly absorbing of certain wavelengths of light. For example, the hemoglobin molecules in blood absorb green and blue light quite strongly, so that they appear red. When you look at a flashlight through your hand, the light appears red because of this absorption of green and blue light by hemoglobin. If you use a bright enough red light source and are willing to look very carefully, probably with sophisticated light sensing devices, you can probably see a little light coming through a person’s body. But that light will probably have bounced several times during its passage, so that you won’t be able to learn anything about what the person’s internal organs look like. To get a better view of what a person’s insides look like, you need light that penetrates more effectively and that doesn’t bounce very often. Moreover, you must employ techniques to that block this bouncing light as much as possible so that you only see light that travels straight through the person. The light that does this isn’t visible light—it’s X-rays. X-rays are very high frequency, very short wavelength “light” (or rather electromagnetic waves). Tissue doesn’t absorb these X-rays much at all and they can go through people to form images.
A rainbow isn’t an image that originates at a specific distance away from your eyes. It consists of rays of colored light that travel at particular angles away from the water droplets that produce them. You see red light coming toward you from a certain angle because at that angle, the water droplets are all sending red light toward you. In the garden hose case, the water droplets are so densely arranged that they are able to create a brilliant rainbow in only a few meters of thickness. In a typical rainstorm, sunlight must travel through hundreds or thousands of meters of raindrops to produce an intense rainbow. When you look up toward the red arc of the normal rainbow, you are seeing light directed toward your eyes by millions of water droplets, some close and others distant, that are all sending a part of the red portion of the sunlight striking them toward you and the other wavelengths of sunlight elsewhere.
You are correct that a normal rainbow is cut off abruptly by the horizon and that it would continue down below to form a full circle if the ground weren’t in the way. People in airplanes sometimes see full 360° rainbows.