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My question is tied closely to this one, asked a while back on the website. As far as my understanding goes, a rainbow is formed by sunlight undergoing two refractions and a reflection inside individual water drops, and then falling on our eyes. An upper drop disperses red light the most, angling it towards our eyes and a lower drop similarly angles the less dispersed violet light towards us, after reflection. However, the way it looks to me is that there's no room for any of the other colours to fill the gap between the red and violet light. That pattern seems to read

vibgyo R V ibgyor

from top to bottom, the bold letter indicating the colours seen upon reflection by us. So where do the other colours come into play here? Also, does this pattern indicate that upon moving up in the vertical direction, we would begin to see the rainbow invert its colours?

Picture from above linked question

Qmechanic
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Kritin Thakur
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3 Answers3

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The diagram produced in the question has a couple of errors and almost answers the question.

enter image description here

To a very good approximation the rays coming from the Sun are approximately parallel and the reflection from the raindrop is not the result of total internal reflection.

The important things to note is that a rainbow as a result of the reflection and refraction due to many raindrops and only the light rays entering the eye produce an image of a rainbow on the retina.

enter image description here

Note the cones of rays which do not enter the eye.

This last image is to emphasise the points about many raindrops producing a rainbow and only the light entering the eye is detected by the eye.

enter image description here

Farcher
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  • That's simply not true,primarily due to the fact that the "droplets" are grossly not to scale compared with the size of the ugly sack of mostly water. It's not like moving your head a bit changes the order in which the colors are observed. What you have is near-plane-wave emission of each color at a slight angle from other colors, and your eye focusses these plane waves by converting angle to spatial position on the retina. – Carl Witthoft May 19 '22 at 13:50
  • I started to write this answer, got distracted, and came back to discover that @Farcher had done it for me. – rob May 19 '22 at 14:03
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    @CarlWitthoft Moving your head doesn’t change the order of the colors, but it absolutely changes the location of the rainbow. The ones made of actual rain are much easier to make if the rain is distant, so the change in location is harder to see than if you make a rainbow with a garden sprinkler. But if you ever do find yourself able to see where a rainbow touches the ground, trying to walk there and catch it is an experience sufficiently interesting to inspire a myth about tricksters and their inaccessible treasure. – rob May 19 '22 at 14:09
  • @CarlWitthoft You are entirely correct about the scale. I tried to use the graphic provided by the OP.I omitted a lot of things including the important idea about the variation with angle of deviation of emitted light intensity with angle of incidence of the sunlight on the drop. My aim was to explain that many drops were involved although there was no way I was going to draw a scale diagram but perhaps more importantly the fact that the eye on senses the light which enters it.I am sorry that I have been "economical with the truth" but that I feel does not warrant a -1 which I assume was your? – Farcher May 19 '22 at 14:38
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When light hits the edge of the droplet (from the inside as well as from the outside), it can undergo a reflection as well as a refraction. So there can be several reflections inside the droplet before the light comes out. Because of that, light is dispersed many directions.

This also explains you can observer a secondary rainbow, which is also a circle (only partly visible, usually) and concentric to the primary one.

Miyase
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The graphics just shows two raindrops, although of course there are lots of raindrops in between those two.

It shows that every raindrop emits a bunch of rays, dispersed depending on the wavelength (color), with violet coming back closest to the incoming ray, and red farthest.

The upper raindrop shown is one where the red end of the spectrum just happens to reflect into the observer's eye, and from the lower one, the violet end just hits the eye. (See below for the sloppy creation of the graphics...)

From the many raindrops in between, some intermediate point of their spectrum (between red and violet) hits the observer's eye, thus producing the well-known continuous rainbow spectrum.

Sadly, the graphics has been created rather sloppily:

  • The red ray from the upper raindrop doesn't hit the guy's eye, but his hair, so this raindrop wouldn't be visible in the rainbow.
  • The violet ray from the lower raindrop doesn't hit the guy's eye, but his mouth, so this raindrop as well wouldn't be visible in the rainbow.
  • The incoming rays from the sun should be parallel - the sun is so very far away that the angle difference between the connections to the two raindrops is below a millionth of a degree.
  • And it would have helped to include a third raindrop in between.
Ralf Kleberhoff
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