The Non-Linear Optics of Interfaces in R^3

Overview

Objectives/Goals To model the distortion of an image through a spherical interface. Methods/Materials Assuming that the object in question is a photograph of a cat composed of pixels, I used trigonometry, geometry, and Snell's Law to obtain a function (the distortion function) that gives the perceived position of the pixel given the original position of the pixel. Then I used Mathematica (a computer program) to model the distorted image of the cat according to how a fish in a sphere of water would perceive it. Results Assuming that the object in question is a photograph of a cat composed of pixels, I used trigonometry, geometry, and Snell's Law to obtain a function (the distortion function) that gives the perceived position of the pixel given the original position of the pixel. Then I used Mathematica (a computer program) to model the distorted image of the cat according to how a fish in a sphere of water would perceive it. Conclusions/Discussion Interfaces of different materials distort images. I demonstrated that, using geometry, programming, and laws of optics, one can model the distortion of an image. As a result, one can find the actual location of an object on the other side of an interface using the perceived (or distorted) location. This can be applied to marine observation.

Competition history

• CSEF 2010 Mathematics & Software · Entry S1699

Resources

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