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Caustics: The Von Seidel equations

Kooij, J.F. (2017) Caustics: The Von Seidel equations. Master's Thesis / Essay, Science Education and Communication.

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We are intrigued by the caustic of a paraboloid. A caustic is the enveloping surface of reflected rays. In 1862 von Seidel stated that in case the reflected rays are obtained by reflecting a bundle of parallel rays in a paraboloid the caustic is given by some easy system of equations, but he never published his derivation of these equations. We took on the challenge to try and set up a derivation that gives the same caustic. This can be done by first getting accustomed with the method in two dimensions. Transferring these calculations to three dimensions gives us the possibility to determine the caustic of a paraboloid. Since von Seidel did not specify how skew his incoming rays were, we can obtain three results. We can either obtain the von Seidel equations, prove that they do not hold, or obtain a representation that does not give any definite answer. This thesis discusses these possibilities and a technique is proposed to verify them, provided they are indeed correct.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Science Education and Communication
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 08:26
Last Modified: 15 Feb 2018 08:26

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