Parabolic Reflector: UNIZOR.COM - Physics4Teens - Waves - Properties of Light
Channel: Zor Shekhtman on UNIZOR Education
Date: 27/01/2022

UNIZOR.COM - Physics through a Looking Glass of Mathematician
Notes to a video lecture on http://www.unizor.com

Parabolic Reflector

Consider now a more complicated case of a curved reflection surface.
Any smooth surface can be considered as an infinite set of infinitesimally small flat pieces with each piece reflecting light in a direction that can be determined by a plane tangential to a surface at that point.
So, to determine the reflected light at some point of a surface we can just replace a surface with a tangential plane at that point and use the Laws of Reflection presented in the previous lecture.

Let's illustrate this on a concrete example of a paraboloid as a surface reflecting the light. Paraboloid is a surface obtained by rotating a parabola z=k·x² in the XZ-plane around the Z-axis.

As a result of this rotation, the three-dimensional formula for a paraboloid is
z = k·(x² + y²)

We will examine how vertically going down rays of light are reflected by this surface.