LTP 126: Rainbows

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In this solo show Bart explains how rainbows work, why that leads to some ‘bonus extras’ to keep an eye out for, and shares some advice on capturing these beautiful and ephemeral apparitions!

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Show Notes (by Bart)

Depending on where you are in the world, your best chances to see rainbows will be at different times of the year, but here in Europe, we’re entering prime rainbow season as those infamous April Showers approach!

Those April shows are so predictable they’ve been captured in the folk aphorism ‘March winds and April showers bring forth May flowers’.

When to Watch out for Rainbows

To get rainbows you need a mix of sun and rain, so showery weather is ideal. Any time you’re in sun and there is rain falling in the exact opposite side of the sky to the sun, check for a rainbow!

Where do you check? Well, because of how they’re created (lots more on that in a moment), Rainbows are always the same size – 84º across the widest point, or about 8 times the width of your fist at arms length – and always entered on the point directly opposite the sun in the sky.

Depending on how much rain is falling over how wide a section of your field of view, you may only see a dim rainbow, or a section of one, but each time you feel the sun on your back while you’re looking at rain, get into the habit of checking for pieces of rainbow!

Also — because rainbows are centred on the point directly opposite the sun, mornings and evening are prime rainbow time, because when the sun is low, rainbows are tall, and when the sun is high in the sky, rainbows are short. In fact, if the run is very high, rainbows may be so short they’re invisible.

How Rainbows Work

Any time the sun is behind you, there’s a potential rainbow in front of you centred on the point directly opposite the sun and extending to a full circle. For some part of that potential rainbow to become real, you need raindrops between you and that part of the potential bow. Since rain can’t fall below the horizon, every part of the potential bow that lands on the ground is ruled out. That means that when the sun is high in the sky the potential bow will be small. In fact, if the sun is high enough, none of the potential bow will be above the horizon! But, when the sun is low the potential bow is big. In spring the sun is still low in the sky, and we get this mix of sun and rain, so it’s prime rainbow season!

BTW, If you’re wondering why rainbows are always the same size, it’s because the size is determined by the refractive index of water (how much it bends light), not the size of the drops!

What’s causing the rainbow is that some of the light from behind you is entering into rain drops in front of you, bouncing off the back of those raindrops, and then coming back to you. Each time light passes from one medium to another (air to water to air in this case), it bends a little, and each frequency, or colour, bends by a slightly different amount, so the light gets spread out. Because raindrops are round-ish, most of the light bounces off the surface of the drops and doesn’t enter it at all, but when the angle is right, some of it goes through, bounces off the back, and then makes its way back to your eye. Because the range of angles where that path of light is possible is small, the end result is a ring of colours with a radius of about 42º (angular width, with a full circle being 360º). When you do the math you find that red light is actually bent to form a circle with a radius of 42.5º, and the blue light it bent to form a circle with a radius of about 40.6º. Anyway, the end result is that you get about a 2º-wide band of colours that makes up a slice of an approximately 84º wide circle (twice the radius!).

What happens all the light that doesn’t line up just right to make it into the rainbow? On average, more of it gets reflected into the bow that out of the bow, so that leads to a really cool effect most people don’t notice until you draw their attention to it — the sky inside rainbows is noticeably brighter than the sky around the edges of rainbows!

I want to draw your attention to the fact that water, like glass, is mostly transparent. Each photo of light that hits the surface of a windows, or a raindrop, has some probability of bouncing off, and some probability of going through. This is why windows have faint reflections! We thing of water as transparent, because the probability of going through is higher than the probability of bouncing. For a photon of light to become part of a rainbow it needs to pass the first time, which is most probable, then it needs to bounce off the back, which is unlikely, then it needs to pass through the front again, which is probably, so it needs to do the most probable thing twice, and the less probable thing once to make it into the rainbow. Most light does not, that’s why rainbows are not as blinding as the sun!

Now — if you angle things just right, it’s possible for a photon of light to pass into the front of a raindrop, hit the back at a shallow enough angle that if it bounces, the angle of reflection will send towards a different part of the back of the drop, so it gets a second chance to bounce, and if it does, then it can come back the direction it came. Because these photons bounce twice, they don’t come out at that approximately 42º angle, the extra bounce shifts their paths a little, so they come out at an approximately 10º higher angle, i.e. spread between about 50º and 53º, so they make a second, outer rainbow with a diameter of about 100º. Also, the extra bounce literally mirrors everything, so now the red is on the inside and the blue on the outside!

The other thing you’ll notice is that if you can see it at all, this secondary bow is always much dimmer than the primary one, why? Because the photo has to win the bounce/pass lottery twice! It still needs to do the most probably thing, and pass through, twice, but it now also needs to do the less probable thing, and reflect, twice, which is just a lot less likely. So much less likely, that if there are not enough raindrops for the light to bounce through, there will be too few photos in the secondary bow for you to be able to see it at all.

Finally, when you’re lucky enough to get a nice rainbow, look carefully inside the primary bow — you might see fine little arcs of light. These are so-called supernumerary arcs, and they’re really cool from a physics point of view. The optics research published by Sir Isaac Newton perfectly explains the primary and secondary rainbows we see, as well as the difference in sky brightness between the inside and the outside, but if his understanding of optics were to be complete, then supernumerary arcs would be impossible! But we can see them, so, the proves there must be more physics beyond Newtonian Physics! The laws and equations Newton used are a good approximation of the real universe, but they’re missing some of the finer subtleties of reality!

It took another few hundred years to figure out what it is Newton didn’t know, but with the help of some quantum physics, those little arcs are now perfectly explained by the laws of physics as we understand them today. The physics of sub-atomic particles is usually pretty invisible to us, but each time you see those little arcs on the inside of a rainbow, realise that without a deep understanding of the physics of subatomic particles, we’d have no idea why they exist!

So, in summary, when you see a rainbow, try see how many of its features you can spot:

  1. The Primary Bow
  2. The difference in sky brightness inside and around the primary bow
  3. The Secondary Bow
  4. Supernumerary Arcs
Photographing Rainbows

Rainbows are wide! So, you either need to shoot with a wide angle lens, or, shoot a panorama of some kind.

When I shot with a DSLR, I needed my trusty 10-20mm ultra wide lens to do them justice. That meant that when I was out and about with just one lens, rather than with my full camera bag, I was often forced to resort to shooting multiple shots with the intention of stitching them together in photoshop. This was always fiddly, and I’m so happy my iPhone has liberated me from that chore! One word of advice I will give — if you want smooth stitched panos, overlap your shots a lot — I tried to always get ⅓ overlap at each boundary.

Now that I shoot with the iPhone I don’t need to worry about not having the right lens with me. The iPhone’s ultra-wide camera just about captures a full double rainbow, but only just, and with very little room to spare. When needs must it’s fine, but the compositions can feel a little cramped, and you end up with too little spare around the edge to do enough perspective correction to get any obvious verticals near the edges vertical again. If you’re shooting in nature that’s often fine, but if you have things like buildings, lamp posts or road signs at the edge of the scene they’ll look terrible!

This is why, when I have the time and the foreground is not too dynamic, I prefer to use the iPhones panoramic mode with the camera held vertically and the ultra-wide lens selected. That lets me paint the rainbow with lots of room on all sides, both for nicer compositions, and, to allow for enough perspective correction to get any verticals vertical.

The only other piece of advice I have while shooting is to flip your camera into raw mode — that goes for DSLRs as well as camera phones that have that capability. You really want to have as much data as possible to work with in post.

When it comes to post-processing, my advice is to start by making sure the white balance is accurate, then, ramp the colour right up, using the vibrancy and saturation sliders if your app has both, and to use a curves adjustment to pull the shadows down and the highlights up in a nice s-curve to help the rainbow ‘pop’. On the iPhone’s built-in editor there is no curves tool, so when I’m editing on the iPhone I start by letting the phone try its best with the auto button, then I assert my will by removing all darkening of highlights and brightening of shadows, adding in plenty of saturation and vibrance, and dealing in a healthy dose of definition. Finally, in some cases, just a little darkening around the edges with the vignette slider can work wonders!

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