My Midnight Rainbow Quest – Tougher Than I Thought

I just recently looked a little deeper into some rainbow geometry and discovered that this challenge could be a lot harder than I first imagined. But for those of you who have no idea what I’m talking about, here’s a little history –

The Facebook Quiz

This all started with one of the little quizzes I put on my personal Facebook page from time to time. This one went like this:

No unicorn questions today, but I do have a short quiz on rainbows for you - During what part of the day will you see the biggest rainbows? A) Early morning B) High noon C) Late afternoon D) Midnight E) All of the above F) None of the above
– 11:59 pm on July 11, 2019

A friend, John Gilbert, responded:

Bogus question, Bruce. Answers D, E and F are unicorn answers. I’ll take B, high noon, for 500.

John Gilbert’s 4:56 pm Facebook comment on July 12, 2019 to above post
To see the Note click here.To hide the Note click here.
Although John was a photographer for the Navy, now he is an artist. You can check out his website www.johngilbertartist.com.


to which I responded,

You started well but still wound up with the fourth-best answer (just behind D)….

My 3:31 am response on July 22, 2019

Then:

A flash photo using a common digital camera of a rainbow is not logical
– 8:50 am on July 22nd
If you are referring to an attempt to capture an existing rainbow, in much the same fashion as all those people who take flash pictures of an event from the nosebleed section of the stadium, I would agree, but at noon (at moderate latitudes) and at midnight, there is no existing rainbow. You would be counting on the flash, placed at the correct angle, to produce a rainbow that your camera could capture. I wouldn't expect it to be easy, but illogical? Are you sure? Even with the ISO cranked way up?
– 10:10 pm on July 22nd
I don't usually photograph rainbows after dark. I've never seen a photograph of a rainbow after dark. If you have one, I would love to see it.
– 6:42 am on July 24th
Put-up-or-shut-up challenges are quite reasonable here. I mentioned that this may not be easy, and I have a lot on my plate right now, but I'll see what I can do. Stay tuned. My first goal will be to make sure it's possible, then we can talk about composition.
– 8:53 am on July 24th
To see the Note click here.To hide the Note click here.
By the way, the correct answer to the quiz could be either A or C. If you can’t handle more than one correct answer on a multiple-choice question, pick C (more large rainbows will be seen then because more people are awake around dusk than dawn). The animation below shows how a rainbow changes with the movement of the sun. (The black face on the ground represents the top of the shadow of the observer.)

animation showing movement of rainbow with sun

The Contest

To speed things up, I then asked our local Kendall Camera Club for help by creating a contest for the best nighttime rainbow picture. I am now extending that contest to all of my readers. Here are the rules:

Contest Rules

  1. I’ll give the equivalent of a six-pack of your favorite brew (within reason) for the best picture of a rainbow at night. I said six-pack equivalent because a corresponding discount for any of the products or services of Bee Happy Graphics (see our Products and/or Services pages) may be substituted at your request.
  2. The contest will run at least another month but may continue until we get a chance to get our own rainbow pictures (which will not be part of this contest), or until I give up all hope of completing this quest. If there are not enough entries at the end of the contest, the prize need not be awarded.
  3. You can enter your image by emailing the file to admin@BeeHappyGraphics.com.
  4. Composition does count. Photos of real rainbows will be given precedence, but just in case I overstated the possibility of that occurring, “Photoshopped” rainbows will be accepted.
  5. I will announce the close of the competition and the beginning of the voting process in a comment to this blog post. I will explain the voting process in that same comment.
  6. At least three weeks after the announcement from Rule 5 above, a winner will be announced. If any entry has three or more votes, the one with the most votes will be the winner. If no entry has that many votes, then I will take an informal survey among my closest family and friends, and pick the winner. The decision of the judges (as defined above) is final. This prize may be combined with other promotions.
  7. Since this is a photo contest, I should mention that the photographer retains all rights to his/her image. We get to use your image only to run and publish the results of this contest.

So far, there have been no entries.

The Physics

As I mentioned at the beginning of this article, the geometry doesn’t look good.

illustration of angle of refraction/reflection of a single raindrop
Figure 1: The average angle between the light source (usually the sun) and your eye from a single raindrop. Because of refraction, the angle for violet light is a couple of degrees less than the angle for red light.

Figure 1 shows the angle that a light ray bounces off of a single raindrop. In Figure 2 (which is a view looking down, with the blue-hashed region being a rain cloud), one can see that as the sun’s rays all come in as parallel lines from the same direction, the five representative raindrops, and all others from which the blue light rays bounce at the same angle into the observers eye are all along the same line of sight, and therefore all reinforce each other. A single raindrop doesn’t reflect a lot of light and it takes the light of a lot of raindrops to make the rainbow visible. Similarly, the raindrops reflecting red light into the eye from a slightly different angle form along a slightly different line of sight and also reinforce each other.

illustration of the geometry of refraction/reflection that causes rainbows
Figure 2: The geometry of light reflected/refracted from a distant source where the incoming light rays are all parallel

The Problem

illustration of the geometry of refraction/reflection caused by nearby light source
Figure 3: The geometry of light reflected/refracted from a nearby light source

But using flash, the geometry is different; the light source and the eye can now be represented by single points. But unless you were the navigator of a Coast Guard buoy tender or something, you may have forgotten a lesson from high school geometry; that the set of all points for which the angle between those two objects is the same defines a circle, not a line. In Figure 3, the angle between the flash and the eye is the same for Representative Raindrops A and B, and all other dark blue points on the outer circle (there is no rain along the pale blue segments of that circle). Unfortunately, each point on that circle is along a different line of sight from the observer and the light rays do NOT accumulate in the eye. To make matters worse, the red light reflected from Representative Raindrop C (on the circle of red light) IS along the same line of sight as the blue light from Representative Raindrop B (and the other colors of the spectrum from raindrops directly between them), which tend to cancel out into white light. This means you will see no rainbow.

Where Does That Leave Us

The original purpose of this article was to throw in the towel and admit defeat, but as I was getting the materials together, I’ve already come up with a couple of new ideas that need to be explored. But the busiest part of our art festival season is now upon us and the rainy season doesn’t start in South Florida until around June, so this is not the rainbow of promise, but one of hope. Stay tuned. (And if you have a photograph of a nighttime rainbow, please send it.) Thanks.

Author: Bruce

Although I grew up in Garden Grove, California, I have lived here in South Miami longer than I've lived anywhere else in the world. I've been married to my wonderful wife, Nancy, longer than I was ever without her. We were both teachers. Nancy recently retired after 40 years. I have also spent time as an officer in the Coast Guard, a commercial property appraiser, and an electrical engineering student. Now I'm technical support for Bee Happy Graphics. That means I handle this blog, our web page, and all E-mail, I do all post-processing and printing of the images, I cut mats and glass and frames. If you have a technical question, I would be the one trying to answer it.

Your "two cents worth" is welcome (but I don't give change).

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