T.2) Making matrices for bouncing light rays off curves

For full understanding, you should be familair with T.1) above.

T.2.a.i)

Here's a curve and a point above the curve all plotted in true scale:

Light rays eminate from the point and hit the curve like this:

Your job is to plot the reflected light rays.  Do it.

Answer:

Throw in these tangential (perpframe[1,t]) and normal (perpframe[2,t]) perpendicular frames:

perpframe[1,t] is tangent to the curve at {x[t],y[t]}.

Now reverse the light vectors:

These are not the reflected rays, but the reflected rays do make the same angle with the plotted normals that these vectors make.
This tells you that to get the reflected rays, all you have to do is to hit the -ray[t] vectors with frame flipper matrices to flip -ray[t] about perpframe[2,t].
  
Here you go:

Note the extra minus sign in the specifcation of the hangerframe.

Clean it up with a plot showing both the incoming rays and the reflected rays:

If you want lengthen the reflected rays, you can.
Just do this:

And you're out of here.