Where is the Rainbow?

An artist's rendering of refraction and reflection in a water droplet. An artist's rendering of refraction and reflection in a water droplet.

When it rains on a sunny day, sometimes we see rainbows—circular arcs of every color from red to violet. When sunlight hits a water droplet, the light bends and is reflected at a specific angle. Different colors of light bend differently, so the droplets split up sunlight into a band of colors.

If the conditions are right, which direction should you face to most likely see a rainbow?

Towards the sun Away from the sun The direction you face doesn't change the likelihood of seeing a rainbow

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9 solutions

Chew-Seong Cheong
Aug 24, 2018

We note that the rainbow is formed on the other side of the raindrops, we are most likely to see a rainbow if we face away from the Sun .

Nice solution sir! By the way, don't know you also master at Physics related problem!

Kelvin Hong - 2 years, 9 months ago

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I achieve level 5 for Classical Mechanics in Brilliant.org. See my profile .

Chew-Seong Cheong - 2 years, 9 months ago

This picture is misleading. You aren't seeing a projection on the sky behind the water droplets, but rather each individual droplet sends a tiny bit of rainbow directly to your eye (if it's at the correct angle)

Jeremy Galvagni - 2 years, 9 months ago

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It is just that I am lack of a proper drawing software. Anyway, I have changed the image.

Chew-Seong Cheong - 2 years, 9 months ago

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It still looks like the water droplet is projecting the sun's rays onto the sky. Ram Mohith's illustration is much more accurate.

Jeremy Galvagni - 2 years, 9 months ago

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@Jeremy Galvagni Sorry, I think I got it now.

Chew-Seong Cheong - 2 years, 9 months ago

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@Chew-Seong Cheong You did. Looks great now. Upvoted.

Jeremy Galvagni - 2 years, 9 months ago

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@Jeremy Galvagni Thanks a lot.

Chew-Seong Cheong - 2 years, 9 months ago

The picture is plain wrong. The viewer would have to turn 180 degrees to see the refracted light as pictured. In fact, the problem is not stated correctly as water droplets are 3-dimensional, thus refracting and reflecting light in many directions, making a rainbow visible from a range of viewpoints, not just "away" from the sun.

Vadim Pshenichnikov - 2 years, 9 months ago

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Thanks, why don't you provide your solution.

Chew-Seong Cheong - 2 years, 9 months ago

Sorry, I think I got it now.

Chew-Seong Cheong - 2 years, 9 months ago

Here are two Korean adages:

"Don't cross the river when there's a morning rainbow."

"Don't tie your cow by the riverside when you see a rainbow in the west sky."

Try and infer that this makes sense from this problem and the climatic and latitudinal condition of the Korean peninsula. :)

Boi (보이) - 2 years, 9 months ago

But water droplets have been studied and proven to be more spherical than..... pointy???..... You get my point. That artistic representation is incorrect!

Christina Cao - 2 years, 9 months ago

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The original illustration was spherical. This one is an "artist's" and not "physicist's" impression.

Chew-Seong Cheong - 2 years, 9 months ago

Most importantly, since your eyes move independently from your head, the direction you face is less important Thant the direction from which your eyes look

Brian Wald - 2 years, 9 months ago

When you can see a double rainbow , the second (upper) one is light that has been reflected twice in the individual raindrops , and the colours are reversed. It's also possible , though very rare , to have a triple!

Devon Fletcher - 2 years, 9 months ago
Ram Mohith
Aug 20, 2018

When right rays hit the water droplets they they undergo total internal reflection. That means they get reflected to the ground. So, it its better to stand in the opposite direction to the sun to most likely see a rainbow.

Why is there total reflection?

Ilann Cote - 2 years, 9 months ago

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Because the angle of incidence is greater than 49 which is critical angle for water.

Ram Mohith - 2 years, 9 months ago
Albert Fisher
Aug 26, 2018

A rainbow is the upper half of a circle whose center is collinear with the sun (behind the observer) and the observer’s eyeball.

Not just the upper half. If there are clouds below the level of the horizon (e.g. if the observer is in an airplane) a rainbow can be anything up to the full circle.

Paul Cockburn - 2 years, 9 months ago
Jay Singh
Aug 31, 2018

You shouldn't look at the sun. Easy.

Yeah! They can do serious damage to your eyes

Mohammad Farhat - 2 years, 9 months ago
Chris Maitland
Aug 29, 2018

The best way to answer this is the most fun. Go outside on a sunny day and play with a hose or sprinkler. The rainbow will form a circular halo centred on the shadow of your head (or really, eyes).

The boring reason for this is that the angle of reflection in the drop is acute.

Vahgar Anaruhk
Aug 31, 2018

becase the screen(ie. clouds) should be in opposite direction from the sun for a real image

Xeeshan Alam
Aug 30, 2018

I used to see Rainbow after rain!😁

Anthony Espinoza
Aug 28, 2018

I just thought that if a rainbow is a reflection then to see it best you would want to face the same direction as what's being reflected (the sun) as much as possible

Renee Xu
Aug 30, 2018

The water would be reflecting the rainbow. If we look at the diagram in the quiz closely, we see that it is reflecting the light.

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