We all know that light follows Rectilinear Propagation and it sometimes bend while diffraction, but i never understand the concept of rainbow and the reason why it is a curve. I have read books and all and everywhere it says that white light passes through raindrops and boom! It is now a circular arc of 7 lights. I understand the phenomenon of refraction and know light of different wavelengths separate when passes through a prism. But after passing through prism, those light travels straight.
But why is rainbow curve? 🌈
In: 21
Rainbows aren’t arcs or curves, [but *cones*](https://lightcolourvision.org/wp-content/uploads/08240-0-A-BL-EN-Rainbows-as-Cones-of-Colour-80-scaled.jpg), which spread out from the viewer in the direction away from the Sun. The main rainbow comes out at angles of ~41-42° (from the line through you from the Sun), and a secondary one at 50-54° to that line (if we have a double rainbow).
Copied from a previous answer (so links might not work and it might not entirely make sense without context):
With rainbows we are dealing with water droplets, and they are (approximately) spheres. We tend to draw rainbow diagrams [something like this](https://en.wikipedia.org/wiki/File:Rainbow1.svg), with a single ray of light coming in at a particular angle, refracting and reflecting, giving the spread of colours. But light from the Sun doesn’t come in as just a single ray. There are rays of light hitting one entire hemisphere of the droplet (as with the Earth – also a sphere – where light from the Sun is always lighting one half). [This diagram](https://en.wikipedia.org/wiki/File:Rainbow_single_reflection.svg) shows a bit more of that, but is still just looking at the light rays hitting the “top” half (and being reflected out the bottom) – there will also be light rays hitting the bottom and being reflected out the top. So going back to that first diagram, while we have that one ray coming in the top and reflecting out the bottom, [we also get something similar coming in the bottom and reflecting out the top](https://i.imgur.com/nIxX4zU.png) (not the clearest diagram, sorry but the best I could do in a few minutes). We focus on this one ray path usually as this one (at ~42 degrees) is the most intense.
And this is crucial for the “double rainbow” effect. The double rainbow is caused by the light rays which reflect the first time they hit the boundary (like the normal rainbow rays) and then also reflect the second time – but that means [they must have come in on the bottom](http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/imgatm/lpath2.gif) ([source](http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/rbowpath.html)).
Anyway. Going back to [this diagram](https://i.imgur.com/nIxX4zU.png), this means that the “rainbow” doesn’t just come out of the droplet at one point, but two points (one “up” and one “down”, assuming this is a vertical slice through the droplet). But the water droplet isn’t a simple 2d system (like our diagram). It isn’t a cylinder going into the screen, but a sphere. [Add in a line through the middle](https://i.imgur.com/k5doVtk.png) and imagine treating that as an axis, holding either ends and spinning the image around so the water droplet becomes a ball. Now the rainbow rays are coming out not just in two vertical directions (42 degrees up and 42 degrees down) but also those two directions horizontally, and at every angle in between. Every way we slice through the droplet, at whatever angle, we get those two rays coming out either side. And that gives us a cone. A complete cone of rainbow rays coming out of our water droplet, at 42 degrees to the angle the sunlight is coming in at. And due to the double-reflection rays we’d get the second rainbow at ~51 degrees, but fainter as each time the light hits the boundary only some is reflected; potentially we would get a third rainbow from the triple reflection, but that light would head out in roughly the same direction as the non-reflected light would, so it would be impossible to see due to the bulk of the sunlight heading that way (as by this point we’d be down to only a tiny amount of light).
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