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Finding coordinates when light hit the surface

Hi all,

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 http://www.mathhelpforum.com/math-he...3e3513f0-1.gif. 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 http://www.mathhelpforum.com/math-he...1b6d5f09-1.gif 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 http://www.mathhelpforum.com/math-he...73bd1a69-1.gif. 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 since extending the line is not really a rigorous proven way. I hope to hear whether is there any alternative better way of finding the coordinates

Thanks and hope for your help :)