### 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.

1. imatfaal on July 27th, 2011

reminds me (probably wrongly) of the conformal mapping in penrose diagrams, and that mad escher woodcut of angels and devils

http://www.hnorthrop.com/escher.html

2. Anonymous Coward on July 27th, 2011

Nice shots! And certainly some of the most physics-y self portraiture I’ve ever seen.

I’ve tried to observe the same thing “in person” by looking up from the bottom of a pool, but the water has always been too choppy to see it so clearly.

3. Rhett on July 27th, 2011

It took me a second to figure out the picture (because I didn’t read the post first). I thought it was some sort of spherical mirror – but I couldn’t spot the camera.

Now I realize what it was, really great picture. So, it was an indoor pool?

4. swansont on July 27th, 2011

Yes, an indoor pool. The black is the ceiling, the yellow is a railing that goes around the facility, in front of the windows of the adjacent rooms (game room, workout room and dining/meeting rooms)

5. bph on July 27th, 2011

Dude that is awesome.
The t-shirt is cool, too.

6. ColonelFazackerley on July 28th, 2011

Nice. I never thought before that a flat surface should give such crazy distortion in an image.

7. Griff on July 28th, 2011

That is the best optics self-portrait.