Double Refractions in a rain drop

Iainp · Post by **Iainp** » Fri Aug 28, 2009 6:08 am

I've taken many photos of raindrops, but this was my first one that had airbubbles in it. It's the view of a garden through a drop hanging off a washing line.

What's really interesting is that the image inverted by the raindrop is inverted again by the air bubbles, resulting in upright final images. The maths of this is beyond me! Also there appears to be another refraction in the top right corner of the large air bubble image, and also on the left side. I suppose these are refractions of the other smaller bubbles in the drop. All the bubbles show "fish-eye" views, with the side of the house visible on one side, trees on the other, the washing line above and land at the bottom.

rjlittlefield · Post by **rjlittlefield** » Fri Aug 28, 2009 7:13 am

Interesting effect, Iain! I'll try to explain the effect later, but I have to run to class right now.

BTW, this topic got entered twice. Apparently the site was slow, and you submitted twice? Anyway, I deleted the other one.

--Rik

rjlittlefield · Post by **rjlittlefield** » Fri Aug 28, 2009 8:55 am

OK, about those maths...

We can actually skip the math. Let's go straight to the physics.

When there is no air bubble, then the front and back sides of the water drop act as convex lens surfaces, which I'll diagram as () . These surfaces are strongly curved, compared to most camera lenses, so the water drop creates a short focal length positive lens. This projects the world behind it to form a small inverted real image slightly in front of the drop.

When there is an air bubble, then we get essentially two more refracting surfaces in the optical path. I'll diagram this as (o) where the little "o" represents the air bubble. These inner refracting surfaces are even more strongly curved than the outer ones. From the standpoint of the water, these even stronger surfaces are concave, so each chunk of water in front and in back of the bubble consists of a strongly concave refracting surface paired with a less strong convex one. Being stronger, the concave surface wins, so the net effect is that the water drop plus air bubble comprises two negative lenses. The combination makes a strong negative lens, which refracts the world behind it to form a small upright virtual image slightly in back of the drop.

So, what the camera see is a combination of four things: 1) far background around the water drop, 2) the water drop and air bubble themselves, 3) the small upright virtual image behind the air bubble, and 4) the not quite so small inverted real image in front of the water bubble. If you shoot with a wide aperture, you'll become painfully aware that the last three occur in different planes and you have to stack to get them all really sharp. In the current picture, apparently you have stopped down far enough that everything is at least sharp enough to be recognizable.

Hope this helps. It's an interesting demonstration!

--Rik

Cyclops · Post by **Cyclops** » Fri Aug 28, 2009 11:15 am

Interesting effect Ian-unfortunately we've seen a lot of rain drops of late!
What we have here is natural ultra short focal length lenses!
They're kinda like fisheye lenses but also they will magnify any object viewed close to them. In fact legendary naturalist and early microscopist Anthony van Leeuvenhoek used them as simple microscopes!

rjlittlefield · Post by **rjlittlefield** » Fri Aug 28, 2009 12:23 pm

Good point, Cyclops.

Spherical lenses have another interesting property. If they're made of material with a high refractive index (twice the surrounding medium), then they become retroreflectors. A light beam entering the front is refracted, reflected from the back surface, refracted again, and re-emerges from the front headed back to wherever it came from. This effect is used to make some kinds of safety equipment like retroreflective paint and fabrics. See Wikipedia.

I see that I neglected to address the "refractions of other smaller bubbles". That's exactly what's going on. From the standpoint of the large bubble, the smaller bubbles are just part of the environment behind it, just like the trees although a good deal closer. Similarly, the virtual images of the far background, formed by the small bubbles, are also parts of the background environment of the big bubble. So they too are dutifully refracted to become part of the image formed by the big bubble.

Of course refraction is not all that's going on here. Each of the air/water surfaces also reflects a few percent of the light that hits it. So some of the incoming light gets bounced off the surface of a bubble, then refracted or reflected by another bubble. This effect is mostly what's responsible for those small bright spots at the left side of the rightmost bubble in the second picture.

Setting up this world and simulating it would be a fun exercise in ray-tracing, for a computer graphics class.

--Rik

Iainp · Post by **Iainp** » Fri Aug 28, 2009 1:27 pm

Cheers Rik. If only my physics teacher had been able to explain things so clearly, I might actually have passed the A Level. Ditto Maths, Biology etc...

Cyclops: I must admit, I took these photos exactly one year ago, so it appears this year is a repeat of last. I heard a great comment on the radio recently "So here we are in August, the height of the Great British summer. And you always know it's the summer in Britain because the rain is SLIGHTLY warmer at this time of year."

Aynia · Post by **Aynia** » Sat Aug 29, 2009 11:48 am

These are great photos.

I must look out for air bubbles in droplets now.!!

Cyclops · Post by **Cyclops** » Sat Aug 29, 2009 11:58 am

Iainp wrote: I heard a great comment on the radio recently "So here we are in August, the height of the Great British summer. And you always know it's the summer in Britain because the rain is SLIGHTLY warmer at this time of year."

Lol thats dead right!

Iainp · Post by **Iainp** » Sat Aug 29, 2009 3:31 pm

Ta! Actually I have another "raindrop with bubble" image, which produced a bizarre optical illusion. I'll dig it out tomorrow.