Aperture and DOF

OK I was in class today and a question came up that even the instructor could not answer. So here it is. Why does a higher f stop give you a deeper DOF. It has a smaller opening. How does the small aperture match up to a wider depth of field, anybody know?:confused:
One student said it is due to the radius of the lens but I brought up the pinhole camera with no lens...help. Yes I have a candy bar bet on this one!

Rick

Notice how pinhole cameras have a very small aperture and nearly infinite DOF.

In order to answer your question you should find a first-year introductory physics textbook and flip to the optics section. There will be nice ray-tracing diagrams and formula derivations that will answer your question.

In the meantime, just remember that a larger aperture (smaller number) gives a shallower DOF and smaller aperture (larger number) gives larger depth of field.

Not the radius of the lens, rather the diameter of the aperture, although he might argue that is what he meant. The circles of confusion resulting on the film plane from a stopped down lens are smaller because the aperture is smaller (narrower angles). CoC size affects DoF, or rather apparent DoF. DoF is a concept based on "acceptable sharpness", so a CoC that is "acceptably sharp" varies with format. There is only one plane of actual focus where the CoC is a point where light rays converge and then diverge. Everything else is actually out of focus to a degree, but narrower angles result in more being within "acceptable focus" because the circles of confusion are small enough that we don't see the area as out of focus (they stay small across a longer distance because of the narrower angle). In the case of a pin hole the CoC is the size of the pin hole, so DoF is actually infinite, but it might help to think of it as "constant" because the CoC's are all relative in angle to the size of the pinhole. The reason you can't use a very small pinhole and very long exposure to have a pinhole camera with small enough CoC's to appear "sharp" is because at a certain point another effect called diffraction comes in to play, and limits sharpness, thereby negating another free lunch... I suppose that's as clear as mud, If I think of something better I'll post it, or someone else will explain better.

The key to the whole thing is understanding "Circle of Confusion". Originally I thought the term referenced the area around my view camera while I was working with it

no explanation needed...just remember it...

I think it's important to understand what you do in photography, if there's a practical application for it.

For example, I am just starting to understand print developers, thanks to a few gentlemen that are very generous with their knowledge. This is knowledge that really helps, because the developer can be tweaked to act different ways for different resulting prints. In the case of lenses and apertures - there's very little that can be done to alter any of the optics... Reading Jason's response upstairs made my entire head a circle of confusion... Optics can be interesting, though, and some people actually do tweak or even build their own lenses with stray lens components and get some wonderful results. There's a guy here on APUG, Mark Sawyer, who does this, and he's posted a few images in the gallery here. They're quite interesting. Jim Galli is another guy who just yesterday or the day before posted something made with a modified projection lens on a view camera, and they were fantastic!
So it's up to you what you want to learn I guess. Just be careful, I don't want to discourage anybody seeking knowledge, but you might be spending time on something that you may not have use for.

- Thomas

Thanks for the insight JB, is sort of cleared things up,sort of. Thomas, this is just of those things that we went, MMMM. Then when the instructor did not know, or she acted like she did not know, it sort of got us curious. Got us thinking.

Rick

And that's why I don't want to discourage you. Critical thinking is one of those things that are so important, and it looks like your class has a good measure of it!

- Thomas

Here are two pretty good explanations with drawings:

http://www.aesthetic-endeavors.com/photo/dof/
http://www.normankoren.com/Tutorials/MTF6.html

Lee

Jason did a great job of explaining it without drawing the path of the light rays, which is the way I usually do it.