# Math Help - Finding the coordinates when light hit the ellipse

1. ## 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