Spherical and Paraboloid Mirrors!

The big concept introduce in high school Physics is the Law of Reflection. So here is a little a bit of a refresher. This Law states for a mirror , angle of incidence and the angle of reflection are equal. Let's make use of this law.
Task 0: create the following Povray scenes
A. Create a spherical mirror with perspective and orthographic projection

Perspective

Orthographic

B. Create a praboloid mirror with perspective and orthographic projection.

    

    Perspective

Orthographic

Doesn't it look Fun? The more you learn, the more fun it gets! It's our promise to you!
Paraboloid is a quadratic surface with a conic section. It could be in the form of elliptic or hyperbolic parabola. Except for parabola the other two have 2 foci. When the light ray passes through one of the focus points then the reflection always passes through the other focus points.

• A parabola has an equation : y = ax² +bx+c
• An Ellipse has an equation:  (x²/a² )+ (y²/b²) = 1
• A Hyperbola has an equation: (x²/a² ) - (y²/b²) = 1

Task 1:
Find the coordinates of the object point P, by backtracking the path of light.

What we know:

• parabolic mirror with focus at (0,1) and that passes from the origin
• perspective camera with a pinhole at (0,-1); image plane at y = -2.

Here is a picture for you guys to follow along with us.

Our goal it to find the coordinates of point P. 

1. We will find the slope of the line with coordinates (x, -2) and (0,-1).
2. Use the coordinates of the focus point  to find the equation of the parabola.
3. Find where the parabola and line intersect to determine the other point in line 2 to write an equation of the lind containing point P.
4. Use the equation of the line contain point P to find its coordinates and the location of the light source
5. Good job! We have worked backwards and located a factor in the process of combining cameras with mirrors.