Building Pinhole: Significance/Meaning of 0.03679 For Focal Length

I have been working on a design for a 3D printed 120 panoramic pinhole camera.
I have come across many formulas for calculating the focal length of "focal length = (pinhole diameter / 0.03679)2", but have no found the significance of 0.03679 and how it corresponds.

Another formula I found is "Image Diameter = focal length * 1.92" on Mr. Pinhole's Design Wizard calculations, and can not figure out why 1.92 is used in the calculation.

I am working out comprehensive details of the camera, but am interested in knowing how and why 0.03679 and 1.92 correspond with these calculations.

Does anyone know why these numbers are significant?

Here's a pretty good explanation. In short, it has to do with the size opening that will best work with the visible light spectrum.
http://pinhole.stanford.edu/pinholemath.htm

I would first decide upon the focal length, and then use http://www.pinhole.cz/en/pinholedesigner/ to determine the optimum pinhole diameter. Mr. Pinhole's approach is simple. He has decreed the most desirable figures for the variables involved in pinhole designing. Pinhole camera engineering should not be thus restricted. Pinhole Designer is more flexible, but assumes the user has a good enough understanding of pinholes to intelligently deviate from Mr. Pinhole's standards. As for the optimum focal length, that depends partly on whether the film is held flat or curved. If curved, it depends on where in relation to the center of curvature the pinhole is placed. Also, the optimum pinhole diameter for a panorama camera will be different for the center of the image than for the extreme ends. There may be as much voodoo magic as precise engineering in pinhole photography. The optimum pinhole diameter has been debated for well over a hundred years. Ultimately, it depends on each photographer's preference, not on hard science.

As for the formula, "Image Diameter = focal length * 1.92," that seems to be one of those standards that Mr. Pinhole has arbitrarily established for a camera that covers slightly less than 90 degrees. With such a circle of coverage, the corners of the image will be exposed almost two stops less than the center. Some photographers have made successful pinhole photographs on flat film covering even a wider angle, and even wider than that on curved film. It's too close to my bedtime to tackle the other formula. An excellent resource on pinhole photography is https://jongrepstad.com/pinhole-photography/pinhole-photography-history-images-cameras-formulas/.

Braden said:

I have been working on a design for a 3D printed 120 panoramic pinhole camera.
I have come across many formulas for calculating the focal length of "focal length = (pinhole diameter / 0.03679)2", but have no found the significance of 0.03679 and how it corresponds.

Another formula I found is "Image Diameter = focal length * 1.92" on Mr. Pinhole's Design Wizard calculations, and can not figure out why 1.92 is used in the calculation.

I am working out comprehensive details of the camera, but am interested in knowing how and why 0.03679 and 1.92 correspond with these calculations.

Does anyone know why these numbers are significant?

Click to expand...

my 2cents are attached

If you start with the old film format diagonal = the "normal" focal length, I think that you can go as short as half that distance with a flat film plane camera design with reasonable expectations. The rest is just math.

darkroommike said:

If you start with the old film format diagonal = the "normal" focal length, I think that you can go as short as half that distance with a flat film plane camera design with reasonable expectations. The rest is just math.

Click to expand...

I'd say that sounds about right. Some of these formulas that use a single magic constant have just combined a suitable light wavelength and other parameters to keep things simple. As Jim notes, and I have commented on in the past, the Mr. Pinhole site uses some assumptions and isn't very helpful as to telling the user what they've assumed. I have found the Mr Pinhole coverage numbers to be somewhat pessimistic relative to my experience. (I usually use Pinhole Designer, but that is only available for Windoze.)

It is inevitable there will be fall-off away from the central axis, the pinhole is becoming an ellipse viewed from off to the side (and closes altogether viewed from 90º off). But an additional cause of fall-off is having a thick pinhole plate. One wants a very thin plate and a clean knife edge to the pinhole.

The main thing to remember is that you can be considerably off from these "optimum" numbers and still get results, maybe even results that you like. The article Ralph posted mentions a slightly different optimum for contrast versus sharpness; so even what constitutes "optimum" is a bit rubbery!

Slightly off the direction here but if it is a "pano" you're investigating do consider a curved back and it won't throw a big spanner in the works but give you a nice image without the distortion a flat film plane gives specially with wider angle focal length.
I would also give paper negs an option & not get stuck with only film as a captor.
Welcome & good luck with the project!