Secrets of The Rainbow

By Sander Lam

I'm sure you have ever seen a rainbow, 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?

In “Secrets of The Rainbow” we will discuss these kind of questions extensively. For the sake of accuracy we will perform some mathematical calculations, at secondary-school level. If you're not a hero at math, you can “read around the formulas”. The main conclusions from the calculations are reproduced in the pictures and the text. By skipping the calculations you won't know how those conclusions were reached, but you will still have a decent idea of how the rainbow arises.

On the internet you can find in many treatments of the rainbow a simple argument that is supposed to explain, without calculations, why the color sequence of the secondary rainbow is the mirror image of that of the primary one. However, it turns out that this simple explanation is wrong. At this point, as so often in life, the intuition is not a reliable guide. By explicit calculations and clear pictures we will step by step explain the real details behind this inversion.

Apart from the rainbow itself, we discuss some related topics, albeit superficially. We take a look at the functioning of the eye, and the interaction between light and matter. We note that our calculations are based on an approximation, geometrical optics, and discuss sketchily some situations where this approximation does not apply.

Finally, we focus on some basic properties of light, and the problematic role of light as the connecting link between the two major contemporary theories: the theory of relativity and quantum mechanics.

• Language: English
• Publisher: Sander Lam
• Release date: Mar 10, 2013
• ISBN: 9781301639908

Sander Lam

In 1984, I graduated in mathematics and physics at the University of Utrecht, the Netherlands. Since then I work in IT. I'm always looking for viewpoints that make the world around me understandable.In "Secrets of The Rainbow", I explain how the rainbow arises. Also, I discuss several questions that easily arise when you think more deeply about the topic. Little knowledge of mathematics or physics is required to understand the explanation. A sound interest in the subject is sufficient.After reading "Secrets of The Rainbow" you will feel enriched by some pearls. The information in this booklet is not indispensable, but gives some extra color to the world around you.--Ik ben in 1984 aan de universiteit van Utrecht afgestudeerd in de wis- en natuurkunde. Sindsdien werk ik in de automatisering. Ik ben altijd op zoek naar gezichtspunten die de wereld om me heen begrijpelijk maken.In "Geheimen van de regenboog" leg ik uit hoe de regenboog ontstaat. Ook ga ik in op enkele vragen die al snel rijzen als je wat dieper over het onderwerp nadenkt. Om de uitleg te volgen is nauwelijks kennis van wis- of natuurkunde nodig. Een gezonde belangstelling voor het onderwerp is voldoende.Na het lezen van "Geheimen van de regenboog" zult u het gevoel hebben dat u enkele parels rijker bent geworden. De kennis uit dit boekje is niet onmisbaar, maar geeft toch extra kleur aan de wereld om u heen.

Book preview

Secrets of the Rainbow

Sander Lam

Copyright 2013 by Sander Lam

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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,