The birth of a rainbow

A rainbow is one of the most beautiful natural phenomena. It never ceases to capture the imagination, symbolising unity and diversity, spanning the range of colours that the human eye can see. It has been the subject of myths and legends, in part because its end is not reachable. Until now. I have captured the birth of a rainbow in a spider’s web spun across some succulents on the ground.

Rainbows only appear to those who can see them. Indeed, if you think about it, you’ll never see a rainbow sideways. Rainbows need an observer to exist. They are the result of (1) the sun, shining behind the observer, (2) rain drops in the air that reflect and refract the light from the sun, breaking it into colours, and (3) an observer to see how that the colours happen to come together, thanks to how they are refracted in the drops of rain. In the small drops of water that form rain, the light of the sun is first refracted because it enters water, then reflected on the back of the raindrop, and then it exits the raindrop on the other side to end up in our eyes, and thus, we see a rainbow:

How light travels through a drop of water.

But how does the light split into colours?

The white light of the sun is the sum of lots of colours emitted by the sun. The straight line that light follows changes direction whenever light goes through a different medium. For example glass, or water.

Refraction, the effect caused by the fact that the path of light changes direction when traveling through a different medium (here: water) causes this knife to look broken.

But the medium that light traverses doesn’t affect all colours the same way. And in fact, blue light is more refracted (its direction changes more) than red light.

This is the bottom of a pool. The surface of the water has a few specs of dirt floating around, and what you see there are the shadows of those specs of dust (among the sand at the bottom of the pool). Because refraction is different for different colours, the blue shadow is not exactly at the same place as the red shadow, which gives these coloured edges to the overall shadow. Next time you are near water and can see the bottom clearly, look out for the edges of shadows!

Now, because the sun is a single source of light, the reflection, then refraction in the rain drops of light creates a bow. Were it not for the ground, you would see a whole circle. Some have seen circular rainbows, from a plane, for example.

Also, because the sun isn’t a single point, but in effect a disk-shaped source of light, that bow isn’t sharply defined either, it has blurry “edges”. In reality it’s made of billions of specks of light, each coming from a raindrop. But our eyesight isn’t focused on the raindrops — they are too small for us to resolve, so the rainbow doesn’t appear as lots of little points of colour but as areas of colour. Because we see it “out of focus”, we see the rainbow as bands of colour like a colour filter on top of the background. (Remember this)

So now, the birth of a rainbow:

I took a picture of little drops of water suspended in the air by a spider’s web. In this first picture, you can see the drops and you can see how, in each drop, there is a reflection of the whole world with the ground in the centre, and the blue sky around it. It’s like each little drop is a little concave mirror, which it is (see first figure above).

Drops of water caught in a spider’s web up close. Some drops are not round, that’s because of the water’s surface tension, another cool phenomenon for another time. But each drop is a little mirror of the whole world.

Then, I took a second picture of the web — this time with a lot of the drops being out of focus. Remember how I mentioned above that the rainbow appears as areas of colour and not lots of tiny dots because our eyes aren’t focused (and can’t resolve) the drops of water in the air? Well the same happens here and amazingly, a rainbow is starting to be born: The out-of-focus droplets (also called bokeh in photography) on the left are more blue, and the out-of-focus droplets on the right, are more red. With so few droplets it is not possible to get the seven colours as distinctly as in a whole rainbow, and the whole bow has a too large radius for us to be able to see both the bow and the individual droplets at the same time, except maybe in a very high-resolution photograph from a sprinkler rainbow (my next challenge!). But here you have it. This is how a rainbow is born in the wild:

Right in the middle there, there is an area that shows, from left to right, more blue refracted light, then turquoise-green, then yellow-orange, then reddish.

In this image, I have covered the other areas of the photograph to highlight the area of interest.

In this image, I have lowered the overall brightness and increased the overall contrast of the original photograph, to emphasise the colours. In particular the red, which isn’t very bright, is more apparent with this treatment. The brightness and contrast change is constant across the photograph, so as to not favour any area over another.

When I first saw this image, I could hardly believe my eyes. I have captured the first glimpses, quite literally, of a rainbow!

You may challenge my awe by saying this is an illusion, so I carried out the following check: The image with lowered brightness turns the large amounts of background green into blackish (though a bit of green remains). I cut out rectangles of the areas I thought were blueish, greenish, yellowish and reddish. Then I applied a colour-averaging filter to them, and I increased the brightness back to the original value. Lo and behold, the average colour (as if the whole bit of image was blurred) does indeed reveal blueish, greenish, yellowish and reddish tones, but still tinted with a bit of green, as expected from the background of green foliage. Then to remove even more of the background green, I worked out the average colour of the entire photograph and removed it from the four test areas. I could probably push with an additional cut on the left of the blueish in an attempt to reveal purpleish, but these results are already clear to me. See for yourselves:

Average colours in the different areas cut from the low brightness/high-contrast image above.

Here, the average colour of the whole image was removed from the averages in those four areas. This reveals a colour residue that confirms my rainbow hypothesis: Blueish on the left, more turquoise next, then beige, then reddish on the right.

Nature is so full of small wonderful surprises that I really wanted to share this. This is indeed the birth of a rainbow!

This is what the proverbial pot of gold looks like and to me this is way more beautiful than a pile of metal. With billions more droplets in the air above this spiderweb, and from further away, I might have seen more of the rainbow, but this intimate view, that I haven’t come across before, leaves me quite inspired. To finish off here are a couple of rainbow images I have taken here and there.

I have lots of photos of little manifestations of science around me. When I see something cool, I tend to quickly snap a photo of it. I hope to have time to share more of this here.

Thanks for reading!