The surface given by parametric equations r(phi,z) = (2*sqrt(z)*cos(phi), 2*sqrt(z)*sin(phi), 2z) is a mirror where 0<z<2 and 0<phi<2pi. A light beam has direction (0,0,-1), and hits the mirror at position (sqrt(z0), 0, z0). Find the direction of the reflected beam, and show that all beams with an incident direction parallel to the z-axis get reflected such that they all intersect the z-axis at the same point irrespective of z0. Find this intersection point.
I don't really know where to start with this. Any help would be appreciated!