Solving similar question like problem 144 in project Euler

Shape and space, angle and circle properties, ...
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Joined: Thu May 27, 2010 1:41 am

Solving similar question like problem 144 in project Euler

Post by euler_rule » Thu May 27, 2010 1:56 am

This is my 1st post and nice to meet all of you :)

I am stuck with the following question. This is a question posted to me by my physicist friend

Attached is the figure of a ellipse with a formula of

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. In other word, it has a horizontal radius of 1.5 units and vertical radius of 1 unit.

Now, suppose I launch a light from the coordinates (-1.5,0.0) at an angle alpha in such a way that the light will experience reflection on the surface. How am I going to find all the coordinates when the light hit the surface.

My approach is to find the derivative. Hence I got

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. Then I extend the line until it hit the surface and I check the coordinates. Draw the tangent line and reflect it with protractor manually.

The process is rather tedious and I am hoping someone can help me with a better solution

Sorry it's my 1st time here and still having difficulty adding the necessary equation.

Meanwhile, does anyone know how to derive the java source code for the ray tracing animation in [link] ... ems&id=144[/link]???? Need a better understanding for my question :)
ray tracing.jpg
ray tracing.jpg (138.56 KiB) Viewed 2538 times

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