Fresnel Reflector

2026-02-04

About a week ago I decided to make a Fresnel Reflector.
So a Fresnel lens is a series of lenses where each lenses has the same focal length, but each piece is shifted off the center. This allows for a lenses with a very large surface area, but prevents the lens from become insanely thick.

So what I wanted to make was a Fresnel reflector, a series of parabolas where each parabola shares the same focal point.

So my original approach as using simple trigonometric approach which seemed to be off some how.

Then I decided to go with the simple parabolic math.... ended up with something that looked correct but as I tweaked the input it didn't behave the way I expected.

Finally I sketched out what I had and explained it to a friend who is very good at math, he simplified the math down to a very simple equation.

(Me explaining the scenario to my friend)

Distance from the focal point = FD
Distance from the center of = Displacement
Width of "slice" = W
H of "slice" = H

FD/Displacement = W/H

so using that equation, I started by keeping the width of each slice = 1

As you can see the slices grew very tall... and become a parabola..

So then we had the idea, to prevent the Hight from growing exponentially
Cap the height and decrease the width of the sections

As you can see this didn't behave well for low values of "displacement"

so finally a simple if statement fixed this problem

Allow height to change at close distances from the center
But cap the height and allow the width to change as we get further away, this lets it approximate a parabola at the center, but as we go further away it maintains the same focal point without the height growing

The results........ I printed my first one with a focal distance of 100mm, placed my phone at the center of the focal point and it had an effect... maybe not as big of one as I had hoped for though. So I tested flipping it around and using it as just a hard flat surface as a control, in this case I placed the phone speaker right against it... and this worked way better.

So my second one had a focal point of 10mm, letting me place the phone right next to it, and using an app that measures decibels, I did a few test using my wife's phone to play music and my phone to measure the volume level ~4 feet away. And it worked ever so slightly better than using the back side, I think if I used a material that had a better sound reflection it would have given better results but it was fun anyways.

Left is the first one with a focal distance of 100mm
Right is the second one with a focal distance of 10mm