
That is all very nice, but you still didn't find the solution, since you need the angle (Alfa), which is the main question in your problem.
What I would do, is project the line (P1,P2) into the plane (using it's normal), that will give you a line on the plane starting at I (the point you didn't use before), and another point E. You can find these points easilly, since they are the neares points on the surface, to each of the P1 and P2 points.
Now you can reduce your problem explanation into 2D
P2
x
P1 /
x /
/
___/______ Plane P
S
NOTE: SideWays View (parallel with the plane)

Looking down on the plane you see something like.
++
 E(P2) 
 x 
 / 
 / 
 / 
 / 
 x S 
 / 
 / 
 x I(P1) Plane P 
++
NOTE: Top View (prependicular to the plane)

Since we know the reflection angles are equal, (your alfas), now it should be simple to find the point, using a 2 equations system (if 3D, then 4 equations). Use Pitagoras theorem, applied to the 2 triangles, formed below the reflected ray and the plane normal, or use the upper Triangle, formed by line (P1,P2) and the reflected Ray.
Hope you get the ideia.
