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Math Help - Finding the coordinates when light hit the ellipse

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    Finding the coordinates when light hit the ellipse

    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 y^2+(\frac{x}{1.5})^2=1. 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 (\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 \frac{x}{y}*(\frac{1}{1.5^2}). 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 matlab code to derive the coordinates with different \alpha values.

    Thanks and hope for your help
    Attached Thumbnails Attached Thumbnails Finding the coordinates when light hit the ellipse-ray-tracing.jpg  
    Last edited by noob mathematician; May 25th 2010 at 12:04 AM.
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