How do i find the focus of a parabola

Question

How can i measure different parabolas.

I am a student in Mrs. Bobbie Thompson's 6th-grade class at Butler Elementary and I am working on a science fair project about parabolic reflectors and how if the different widths of a parabolic reflector change the heat of the focus. As a part of my research process Need to get information from an expert in my field of study. therefore I was hoping you could provide any extra information to help me better understand my project.

Answer 1

Hi Holden, great project and you are way ahead of your age for this stuff. With all parabolas, there is a focal point, that is a point that no matter what direction a ray of energy is coming from and no matter where it hits the reflector, they all meet at the same point. That is why when you see satellite dishes, there is a bulb in the center, that is the focal point of the entire curved dish. This means that the energy at that focal point is not related to the shape, but the area it covers.

Imagine if you shine a light from directly above the reflector, the important area is not the surface area, but the area projected on the ground. Thus a steeper sloped reflector doesn't necessarily collect more or less energy. Ideally you would want a flat reflector that has the minimal amount of material and covers the most area, but this doesn't work because there is no focal point for a flat surface.

Thus the best reflector is one that is flatter (not steep sides) so that it covers the most area and has the most energy, but not too flat so that the focal point is still close to the reflector. To further maximize energy concentration, you just continue to make the reflector bigger and bigger.