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How can I calculate for a given lens, where in the periphery a theoretical lens hood would become visible?
This seems dependent on the size of the front element, focal length, and possibly other factors I don't understand.
I build attachments for the front of my lenses to shoot through and selecting the appropriate lens has become challenge because I don't understand this relationship. Thanks!
Angle of view is determined by (real) focal length and sensor/film size. That's your starting point.
where:
For a circular hood you would use the diagonal measure of the sensor/film
For a "petal" hood you would need to calculate based on the width and height as well as the diagonal of the sensor/film.
For many lenses aperture and/or focus distance can also play a part if lenses "breathe" (change focal length) as they are stopped down to different apertures and/or focused to different distances. Sometimes this can be rather significant. The AF-S Nikkor 70-200mm f/2.8G VR II, for example, gives an angle-of-view when zoomed to 200mm and focused at the minimum focus distance that is equivalent to a 140mm lens focused at infinity!
An alternative to calculating fields of view and angles/lengths is to download patterns for different lenses from the following:
Even if you can't find your exact lens, lenses with similar focal lengths/angles of view and front element diameters should be similar.
Disclaimer: this is not exactly an answer to the question, as it doesn't rely on calculation, but experimentation.
I used a do-it-yourself approach for checking lens hoods (and vignetting, to some extent), back in the analog times.
From cardboard, I cut out a 24*36mm rectangle and glued together a box to hold that cutout at the correct distance from the lens mounting flange.
When looking from the back through the cutout into the lens, no part of the lens hood should be visible. If it's visible, estimate the percentage of area obscured by the hood, with 50% covered resulting in 1.0EV vignetting.
Regarding lens vignetting: when looking along the center line, the shape of the lit-up area always looks circular, and that's the reference. Lenses with a vignetting problem can typically be identified when looking from a corner angle: the shape no longer is circular, but looks like the intersection of two overlapping circles: like an ovoid with two sharp edges.
If you aren't afraid of spending some time with cardboard, glue and sharp knives: build a cardboard box with depth equal to the flange focal distance of your camera system, with a front cut out to match the camera/lens mount, and a back coutout resembling your sensor size.
2020's high-tech-version would be to design and print it in 3D.
