Why Rainbows are curve if light travels in a straight line?


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

The whole sky should be a multitude of the 7 different colours in my view, rain doesn’t fall in an arc, rain falls everywhere, so this is a question I’ve always wondered too 🤣

The rainbow is visible as a curve because it’s actually a circle around the sun. Basically the entire sky is scattering light but you can only see the rainbow effect in the part of the sky that forms the correct angle from the sun to the sky to your eye.

This is also why rainbows move as you do, they’re defined by your positional relationship with the sun, as you move that relative position also moves.

The roundness is because the source of the light is from the sun which is also round. The rainbow itself is only a “bow” because you are typically viewing it from the earth where the lower part of the bow get’s cut off. If you were very high up, you would see a circular spectrum (a raincircle?).

Rainbows are actually circular.

It is just that usually half the circle is below the horizon.

The way rainbows appear is that the center of rainbow is on the exact opposite direction of the sun from your head. Meaning that the sun will be behind you when you look at an rainbow.

The thing is that the rainbow is not actually there.

What is there is a bunch of water drops suspended in the air that reflect light coming from behind you back into your eyes.

since the drops are round and light gets reflected at slightly different angles depending on the wavelength you get what looks like differently colored concentric circles.

The rainbow isn’t really there and there is no put of gold or home of the Norse gods at the end.

The light goes more er less straight from the sun, though the air into the water and back into your eyes.

It is just that ever times it switches medium like nothing to air or air to water it has a little change of direction (which is why things underwater look to be in a different place then they are). that change of direction is different for different colors so you don’t just see a single white ring, but a rainbow.

First of all, light doesn’t always travel in a straight line, it can be *bent*. For example, put a straw in a cup of water, then look at it from the side. Notice how the straw in the water doesn’t seem to connect with the part in the air? That’s because light is being bent as it hits the water.

A good analogy would be in imagine a rolling log on a street. Then part of the log hits a patch of grass and the log starts to spin, because the log can roll faster in the street than in the grass. The path of the log is being bent just light light can be bent when it hits a different material.

In the case of a rainbow, imagine a prism sending out light of different colors. Put a piece of paper in the “blue” light, that’s your “eye” seeing the blue part of a rainbow in the sky. Now move the prism around, depending on how you move it the paper might see “red” or “green” or nothing at all if you’ve moved the prism so that it doesn’t cast it’s colors on the paper any more.

If you did the experiment properly, you’d discover that there is a certain amount of left-right movement you can do so that each of the colors falls on the paper, beyond that movement the light misses the paper and you can’t see it. Additionally, there is some some up/down motion you can do so that the colors still fall on the paper.

What I’m trying to explain is if you made a “map” of all the left/right and up/down places you could put the prism to still have the colors it casts hit the paper, you’d get an arch.

When you have water droplets suspended in the air they act as tiny little prisms, spreading out their colors. Instead of moving a single prism, all the water droplets act as a series of tiny prisms, each casting their colors at the same time. Just like in our experiment (only with your eyes instead of paper) the rainbow you see is the combination of all the lights and colors from all the prisms at the same time. And guess what, it looks like an arch.

In short, you see a rainbow as an arch because that’s the water droplets in the arch form the “series of prisms” that your eye can see from where you’re standing.

What happens is light will bounce inside tiny droplets of water suspended in the air. This will send back light with a different direction from which it entered, and this change tends to accumulate light in a specific direction. This direction is defined by the angle between the entering light and the one exiting, and will varies gradually with the light wavelength, so colors end up separated.

Then imagine yourself looking at the sky. The light from the sun can be seen as coming from a single direction, since the sun itself is very far. if your gaze is like a straight line, all the parts of the sky that sits on the special angle between it and the sun direction form a cone.

The reflected light will come from this cone, and from your point of view create a circle. Of course most of the time you will see only half of it and it becomes the very well known bow.

The light that was accumulated into the rainbow will not be visible at other angles, and this creates darker parts of the sky near the rainbow itself.

[A very complete explanation can be found here](https://www.youtube.com/watch?v=M90XEREe66s) (expect a bit of math)

I think because we are here talking about the natural rainbows which we see near waterfalls or after rain is that because our earth is oval somewhat and due to the curvy atmosphere it appears to be curved rainbow…

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).