![\"\"](\"http:\/\/blogs.scienceforums.net\/swansont\/files\/2011\/07\/SnellCircle415.jpg\")
<\/a><\/p>\nThat’s me (I’m the one in the “Make it look like an accident”\/Humpty was pushed t-shirt<\/a>) 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.<\/p>\n 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.<\/p>\n Snell’s law tells us that<\/p>\n <\/p>\n \\(n_1sintheta_1 = n_2sintheta_2\\)<\/p>\n <\/p>\n Water has an index of refraction of 4\/3, so light with a grazing incidence to the water (n=1 for air, and sin(90\u00ba)=1) will be bent to about 38.5\u00ba \u2014 arcsin(3\/4) \u2014 with respect to the normal (perpendicular to the surface) so it acts as a wide-angle lens with a 97\u00ba angle into the camera. Outside of that circle what you are seeing is light from inside the pool undergoing total internal reflection \u2014 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. <\/p>\n","protected":false},"excerpt":{"rendered":" I was on a mini-vacation this past weekend, escaping the DC heat by going to a place that was only slightly less miserable (~95\u00baF instead of 100\u00baF) but I did have the benefit of a pool in which to do … Continue reading <\/a><\/p>\n