Secrets of The Rainbow

Secrets of the Rainbow

Sander Lam

Copyright 2013 by Sander Lam

Smashwords Edition

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Contents

Dive into the Rainbow

Simple Explanation

Figure 1a: fanning of red light

Figure 1b: fanning of green light

Figure 1c: fanning of purple light

Figure 1d: combined fanning of red, green and purple light

Figure 2: what color you see depends on the viewing direction

Remarkable Features

Simple Explanation 2.0

Figure 3: The path of a ray of light through a droplet of water

Secondary Rainbow

Figure 4: the path of a single ray of light which is reflected twice

Figure 5a: fanning of red light (N=2)

Figure 5b: fanning of green light (N=2)

Figure 5c: fanning of purple light (N=2)

Figure 5d: combined fanning of red, green and purple light (N=2)

More Rainbows

Zeroth Rainbow

Figure 6a: fanning of red light (N=0)

Figure 6b: fanning of green light (N=0)

Figure 6c: fanning of purple light (N=0)

Figure 6d: combined fanning of red, green and purple light (N=0)

Sequence of Colors

Figure 7a: directions in which light leaves the drop after 1 reflection

Figure 7b: directions in which light leaves the drop after 2 reflections

Figure 7c: directions in which light leaves the drop after 0, 1 or 2 reflections

Figure 7d: directions in which light leaves the drop after 3 reflections

Dispersion

Figure 8: dispersion through a prism

Colors

More Secrets

Secrets of the Light

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Dive into the Rainbow

Let's talk about the rainbow. I'm sure you have ever seen one, and maybe you even have a general idea of how it arises. But how thorough is your knowledge of this phenomenon really?

Perhaps you know that sometimes the rainbow is accompanied by a second rainbow. But do you know whether there is a third rainbow? If there is, in which direction is it, and why do you never actually see it? Or, if there is no third rainbow, why are there exactly two rainbows? Why is the area between the first and second rainbow relatively dark? Why is the sequence of the colors in the second rainbow reversed relative to the first one? What are supernumerary rainbows, and how do they arise? What does the rainbow tell us about the properties of light and matter?

These are the kind of questions that we will discuss extensively. For the sake of accuracy we will perform some mathematical calculations,