Why Some Rainbows Turn White

0:00 This video is sponsored by Opera.

0:01 More about them at the end.

0:03 When I took this photo, I didn't know

0:05 what I was looking at.

0:06 It seemed like a rainbow except with all of its color drained away,

0:09 like a shadow or a ghost.

0:11 Ghost rainbows like this are technically called fog bows.

0:13 And fog bows form in almost the exact same way as regular rainbows,

0:17 except for one key difference.

0:18 They only form around Halloween.

0:19 Uh, no, it's actually that the water droplets are around 10 to 100 or

0:23 more times smaller than those in a rainbow.

0:25 And that's what makes all the diffraction.

0:26 I mean, all the difference.

0:28 So, let's get into how smaller droplets remove the color from a rainbow.

0:31 There are some great in-depth explanations for rainbows,

0:33 so we won't get into the details here, but the

0:35 relevant summary is this.

0:36 When sunlight strikes a drop of water, some of it reflects backwards

0:39 off the insides of the drop at a bunch of angles,

0:42 but most brightly at around 140°.

0:43 The exact angle depends on the color,

0:45 with bluer light bending the most and ending up closest to 140°, while

0:48 redder light bends the least.

0:49 The result is that white light gets spread out into a rainbow-like

0:52 spectrum of colors when it reflects off the inside of a raindrop.

0:54 So, if you look up at the sky at

0:55 a collection of drops,

0:56 when you look up at an angle of 42 degrees relative to the direction

0:59 of the sun, you'll see redder light coming from those drops.

1:01 And when you look at 40° relative to

1:02 the sun, you'll see bluer light with the other

1:04 rainbow colors coming from drops in between.

1:06 And there you have it, a nice rainbow,

1:08 except light is a wave, and waves can interfere with

1:10 each other and themselves,

1:11 which messes up the perfect light ray picture we just presented.

1:13 In the case of the reflected light from a raindrop,

1:15 the physics is similar to what happens when you

1:17 shine a light through a slit.

1:18 Since a reflection off of a small object isn't that different than

1:20 sending light through an opening,

1:21 the size of the object from the opposite direction.

1:24 With a slit, interference happens because waves passing through different parts

1:26 of the slit alternately add up or

1:28 cancel out and create what's called a

1:29 diffraction pattern of bright and dark spots.

1:31 And with a small

1:32 object, it's the reflections off the different parts of

1:34 the object that add up and cancel out.

1:35 The effect on rainbows is that instead of a

1:38 drop just reflecting back bright light at around 140°,

1:40 there are a bunch more bright reflections at more extreme angles.

1:42 And this means that each color

1:44 doesn't just appear as a single ring,

1:45 but instead a bright outer ring and a progressively fainter

1:47 series of concentric inner rings.

1:49 The reason we don't see concentric rainbows is because of a key

1:52 property of diffraction patterns.

1:53 A wide slit will have lots of narrow, closely spaced bright spots,

1:57 while a narrow slit will have wider, farther apart peaks.

2:00 The narrower the slit, the broader

2:01 the diffraction pattern.

2:02 The wider the slit, the tighter the pattern.

2:04 And the raindrops in normal

2:05 rainbows are the equivalent of very wide slits.

2:08 For a rainbow formed from raindrops a millimeter

2:10 or larger in size,

2:11 the diffraction pattern is so narrow that the effects of diffraction are

2:14 essentially absent, and you get the crisp, high contrast stereotypical rainbow.

2:17 But for drops a bit smaller than a millimeter,

2:20 the diffraction pattern creates concentric rings for

2:21 each color that are far enough apart to create

2:23 extra repeating colored arcs on the inside of

2:25 the original rainbow.

2:27 These are so-called supernumemerary bows.

2:29 With even smaller water droplets around a 20th of a millimeter,

2:32 the rainbow and supernumerary bows get even broader

2:34 and even farther apart.

2:35 But crucially, different colors of light are still only bent away from each

2:38 other by the same amount as before.

2:40 And so the broadening of the rings causes colors to blur

2:42 into each other, making the rainbow less vivid.

2:45 Eventually, with super small water droplets,

2:46 a few hundredths of a millimeter,

2:48 like you get in fog, diffraction causes all the individual colors

2:51 to broaden out so much they pretty much completely overlap

2:53 and add back up to the same original color

2:54 of sunlight as they started.

2:55 White light.

2:56 You can see the same thing happen if you look at red,

2:58 green, and blue colors through an out of focus lens.

3:01 They blur together into white.

3:02 A fog bow is still basically a rainbow caused by the same physics,

3:05 but it's one that's had the

3:06 color blurred out of it by diffraction from the tiny fog droplets.

3:10 P.S.

3:10 If you take just a single

3:12 slice from a rainbow and plot how the rainbow

3:14 changes as the water drop size gets smaller,

3:16 you get a really cool diagram.

3:17 On one end, we have slices corresponding to the purest

3:19 colored rainbows, and on the other end,

3:21 slices corresponding to pure white fog bows with all the

3:24 other varieties of rainbows with supernumemerary bows in between.

3:26 It's a true opera of colors,

3:28 which brings us to today's sponsor, Opera.

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