Once Again, as the Filmosaur among the digital brain trust I find I must totally disagree with both the methodology and the conclusions in this discussion thread with respect to the effect of a single element diopter combined with a wide-angle lens.
I have dug out my B&W diopters - 77mm +2, +3 and +4. And placed them (on land) on my own Nikon 17-35mm f2.8 lenses. Yes, lenses - I have two. And as near as I can determine using a tripod to allow me to have my camera in a fixed position, the doipters do NOT diminish the angle of view of the lens at all. Not at 35mm nor at 17mm.
My results seem to be very different that PGK who gives reductions in coverage in there different lenses he examined. And in the example of the +3 diopter he says that on the 24mm lens he feels the angle of coverage is reduced to only 85% of the same lens without a diopter. PGK also says, "I just talked to a friend about this - he's a lens designer. He confirmed that field of view will diminish if a diopter is used on a wide-angle lens."
And further says, from "The Photographic Lens" by Ray again: "...the focal length of the combined lenses [diopter & camera lens] is less than the prime [camera] lens value...".
In a sense I agree with the last statement by Ray. That "the focal length of the combined lens is less than the prime lens."{ I disagree with PGK's interpretation of this. To me if you say the focal length of the combined optic (lens & diopter) is less than the prime lens. Eg changes from 24mm to less. Maybe 20mm? Then the combined optic according to Ray should gain in angle of coverage, be wider, not be reduced.
As I wrote in my last post, I was unable to find my ancient split diopter, what I did find was a picture taken with the split diopter in 1984, Canon F1, 20mm f2.8 lens, and a series 9 Tiffin split +3 diopter taped onto the lens and put in an Ikelite housing with the standard Ikelite 6" dome, which was all they sold at the time. Unfortunately there are no perfect poles or lines going from underwater to above water. But if I look reasonably carefully at the bars in the grating on the right side of the image. And at the shadows to the left of image center. The only conclusion I can come to is that the underwater part of the image is a little wider than the above part. And since the lens is at the same focus point, the only significant difference is that the lower half of the image has the +3 diopter and the 6" dome port with its attendant virtual image. The above water half of the picture also has the same dome, but the lens is focusing on the real subject at the actual distance.
IF my analysis of the shot is right - that the underwater part of the image is WIDER, it also verifies what I suggested previously, that Frinks pool test methodology was flawed. As were the conclusions drawn from it.
And that in fact, the addition of a +3 diopter INCREASES the angle of coverage of the lens.
Look at the shot carefully and see what you think. Fred