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Non-Linear Optics of Interfaces in R^3

Abstract

The objective: The objective was 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.

This Mathematical project modeled the distortion of an image through a spherical interface.

Science Fair Project done By Anastasia L. Reshetikhin