Gulp

Gulp

‘Gulp’ is a short film created by Sumo Science at Aardman, depicting a fisherman going about his daily catch. Shot on location at Pendine Beach in South Wales, every frame of this stop-motion animation was shot using a Nokia N8, with its 12 megapixel camera and Carl Zeiss optics. The film has broken a world record for the ‘largest stop-motion animation set’, with the largest scene stretching over 11,000 square feet.

Poolside Optics

I was on a mini-vacation this past weekend, escaping the DC heat by going to a place that was only slightly less miserable (~95ºF instead of 100ºF) but I did have the benefit of a pool in which to do a little physics demonstration.

That’s me (I’m the one in the “Make it look like an accident”/Humpty was pushed t-shirt) waterboarding my camera. I set my GOPRO (in its waterproof case) to the time-lapse setting rather than the timer so it would take the pictures automatically as I immersed and panned it, and I wouldn’t have to keep disturbing the water’s surface to reset anything.

What you are seeing here is an effect called Snell’s Circle or Snell’s Window: the light from outside the pool refracts as it enters, and this bending means that the entire view of the outside is compressed into a cone.

Snell’s law tells us that

 

\(n_1sintheta_1 = n_2sintheta_2\)

 

Water has an index of refraction of 4/3, so light with a grazing incidence to the water (n=1 for air, and sin(90º)=1) will be bent to about 38.5º — arcsin(3/4) — with respect to the normal (perpendicular to the surface) so it acts as a wide-angle lens with a 97º angle into the camera. Outside of that circle what you are seeing is light from inside the pool undergoing total internal reflection — the camera is immersed only about 10 cm or so, and the blue you are seeing is from the sides and bottom of the pool.

See the Music

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Cool effect. Since this is not slow-motion, you might think it has to be basic aliasing: seeing a beat between the oscillations of the string and the frame-rate of a camera, often seen with wheels that look to be spinning slowly — or backward — on film. It’s not unlike the effect of a strobe light* that’s near the frequency of oscillation that make the motion seem slow or nonexistent, which sometimes happens with fluorescent (or rectified LED) lighting.

But it probably isn’t, or at least not in a simple way. When you strum a guitar the oscillations have a much longer wavelength. The fundamental mode is a standing wave where the string makes a half -wave (e.g. a 1m string has a wavelength of 2m), and there two nodes, one at either end. The next mode would have a node in the center and be a full wavelength. If the speed of sound is around 400 m/s, that gives a frequency of 200 Hz, or 400 Hz for the 2nd order mode. That’s about what we are hearing. The wavelengths shown in the video are much shorter, by more than an order of magnitude, and perhaps two. 20,000 Hz is way off. Plus the waveforms — you could get them by adding Fourier components, but that’s not going on here. This is a shutter effect, so it’s related to aliasing, but the sampling is happening as the exposure is scanned, i.e. each exposure is taking some time, and the exposure on the left side of the image does not represent the same time as the exposure on the right. This is called a rolling shutter and can have some pretty neat effects.

*Just bought a strobe. So I’ll be playing around with it.