Every explanation of rainbows being taught to innocent (actually not so innocent) children is just an oversimplification of the actual doldrum of the concept. Just a serene explanation that states: “Rainbows are formed when the white light passes through the raindrop, and the drop acts as a prism producing the different colours” Okay… but now that you are a sensible adult, how can we justify that one would never see a rainbow when looking in the direction of the sun? And why is it darker above the rainbow and lighter below it? (It is clear that Awan and I have watched a lot of rainbows.) So you understand, some questions are not answered by the oversimplified explanations your 7th-grade science teacher gave you. Let me promise you that we will delve deep into it, just like the Minecraft achievement “we must go deeper” because the full explanation is so satisfying that it widens our brains. So, let's begin, shall we?

So, for a rainbow to be formed, three things are required: a raindrop, the sun and you (the observer). Sunlight travels in parallel rays due to the sun's distance. When these rays encounter a raindrop, some reflect off its surface while others refract and pass through. Whenever the light goes from one medium to another, some is reflected, and some is transmitted. The amount of reflection and transmission mainly depends on the angle of the light, its polarisation, and the nature of the two mediums. To make your concept more steady, it is essential to understand that when light changes its mediums, there is a change in the speed of that light, which refracts, but why is that so? For example, when the light enters a glass sphere, it bounces up and down. A new charge encounters it, and the wavelength of that electro-magnet length is reduced just as someone is kicking it together, and because the frequency would remain the same, the shorter wavelength would decrease the speed of the light. Just one more thing: The speed of light in a vacuum/The speed of light in a medium is known as the refractive index. With all this, when the light enters a new medium, the angle of that light is essentially changed, got it? Huh? Good enough!

Now that we understand refraction, let’s look at how geometry shapes the rainbow’s arc. A caustic is a bright pattern formed when light rays concentrate, often caused by curved surfaces. This concentration of light is what creates the beautiful patterns we see. For a rainbow, the brightest point, where the light focuses the most, occurs at an angle of 42 degrees below the horizontal. You might wonder why the refracted light stops at this angle and doesn’t go further. So, boys and girls, you should have concentrated more in that math class because here comes the geometry part. As the light goes up, the sphere hits the upper sections of the sphere. Although the ray reflected would refract down, the point on the back of the drop/sphere where it reflects would move up until you get to the very special point, around ⅞ the radius of the sphere/drop. Here, the angle of incidence is so steep that the refracted ray starts hitting the back lower rather than going lower, and that is why the reflection turns around, and we get this 42-degree maximum scattering angle. Here comes one more interesting thing: are you with us? Oh, here you are. So I just rumbled about the 42-degree scattering angle, but it is essential to know that the precise scattering angle depends on the type of light because each light has a different frequency; so, for example, blue light would make the charges go up and down more frequently than yellow light. This means that the light would produce a higher amplitude of electromagnetic radiation, which would result in a more significant phase kick, which would reduce the wavelength more and thus would result in a slower speed for higher frequency lights than the lower frequency lights. Now, the main question is how the rainbow is formed. When the lights reflect, they all do so at somewhat different scattering angles, but the max is 42. So now, when they reflect, they all are projected accordingly; also, one more interesting thing is to imagine that all the colours are lines. Red is the longest, then blue, then yellow, and all of them are placed upon each other now from the start. The middle of that line would be all mixed lights, but the end is the real thing: a small part of red will be shown longer than blue, and some part of blue will be shown because it is longer than yellow.

Last part, how do you see the rainbow? There are billions of raindrops projecting a rainbow cone towards the sun, so how does this allow a unified rainbow to form? So for your eye to see a colour, for example, red, the red caustic should directly go into your eye, and this would only happen when the angle from the Sun to the raindrop to your eye is 42 degrees, and this explains why rainbows take an arch with a 42-degree angle!

In essence, rainbows are a stunning phenomenon arising from the interplay of sunlight, raindrops, and observer perspective. Their beauty lies in the precise physics of refraction, reflection, and dispersion, and we hope that this article clarifies your understanding more!