Our world is illuminated by light. Sometimes, we are stunned by the colors that we see: sunsets and rainbows, flowers and birds. I have previously written about how the sky changes colors, from blue in the day to the reds of sunsets and sunrises. In that post, I also discussed how objects that don't emit light, such as flowers, get their colors. But what about atmospheric phenomena like rainbows?
Most people have seen a rainbow, whether it was a true one created on a sunny, yet rainy day or one that appeared in the mist from a hose or waterfall (as seen above) on a bright day. What is the common theme here? All of these rainbows were formed with water droplets and sunlight. Now, the question is how do the water droplets interact with the sunlight to produce such a beautiful spread of colors?
When we discussed sunsets, we found that they were mainly created by scattered light. However, if the water droplets are just scattering light, then we would expect to see rainbows whenever there are both sunlight and water droplets. But rainbows don't take up the whole sky and only form on some occasions, so this is likely not what's happening here. In that case, what else do we know about light?
Light is what physicists call an electromagnetic (EM) wave. There are many different types of these waves, most of which can't be seen by people. When all types of EM waves are grouped together, we call it the electromagnetic spectrum. The part we see is the visible light, or more commonly just called "light". Other types of EM waves include infrared, which is used to locate warm bodies in dark places, and microwaves, which are used to heat up your lunch. The visible light part of the spectrum contains all of the colors of the rainbow. When these colors are combined together, we see the light as being white. Now, this should give us a clue. The white color of the sunlight shines on water droplets to produce a rainbow with an array of colors. Maybe the water droplets can separate the white sunlight into its component colors? But, how could it be done?
You've probably heard about the speed of light, the ultimate speed limit of the universe, and may even know its value. However, the speed of light value is only valid for light passing through completely empty space, aka vacuums. When light passes through an object, such as a window, the atoms that make up the object slow the light down to a lower speed. The ratio of the speed of light in a vacuum to that in an object is called the index of refraction. The value of this ratio depends on the properties of the material from which the object is made. Another special property of this ratio is that it is affected by the frequency, or color, of the light. Now, you might be thinking, "Hold on. What is this 'refraction' that the index is referring to?" Well, that's the last piece of the puzzle.
In the sunset post, we discussed how light rays can be reflected and scattered. However, the rays can also be refracted. In general, light rays travel in a straight line until they hit an object. Upon hitting an object, they will usually be absorbed or reflected. This is how the object gets its color. But if an object is not opaque, some of the light travels through it. Remember how the speed of light depends on the material that the light is traveling through? When a light ray passes from the air into, say, a window, its speed is lowered. The change of speed causes the light ray to bend. This bending at the boundary between two different materials is known as refraction. As soon as the light leaves the window and re-enters the air, its speed increases and causes the ray to refract a second time. If you know the index of refraction for the two materials and the angle with which it hits the boundary between them, you can actually calculate the angle at which the light will bend. Since water droplets are not opaque, light can travel through them. Because water slows down the speed of the light, the rays will bend when they enter and exit the droplet. So how does this process result in a rainbow of color?
If you look two paragraphs up, you'll recall that I said the speed of light through a material is dependent on its color (or frequency). Since red light has a lower frequency than blue light, it will travel faster through the droplet and bend less. This effect can also be seen with prisms, which are constructed to disperse light. In other words, they are made to break light into an array of its component colors - just like a rainbow.
Now, rainbows are a bit more complicated than a simple prism. After the light ray enters the water droplet and refracts, it then must reflect off of the opposite side of the droplet before exiting and refracting again in order to form a rainbow. Secondary rainbows can appear if some of the light reflects twice before exiting. For this entire process to happen, there is a limited range of angles at which the light rays must enter the droplets. Therefore, the sun must be in the right position relative to the water droplets for it all to work. This is why we don't see rainbows every time it rains on a sunny day.
References
Hyper Physics: Electromagnetic Spectrum by C.R. Nave at Georgia State University
Index of Refraction and Snell's Law by Eric Weisstein and Wolfram Research
Rays Through a Large Raindrop by Les Cowley
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