Exploring How f-Number Affects Depth of Field

[JSGandora]

Homework Statement

Why is the depth of field greater, and the image sharper, when a camera lens is "stopped down" to a larger f-number? Ignore diffraction.

Homework Equations

f-number=f/D where D is the diameter of the hole.

The Attempt at a Solution

At a larger f-number, the diameter of the hole is smaller so there is less exposure, although I'm not sure what that has to do with the depth of field. Can someone help me?

 

[DaveC426913]

If you drew a diagram of light rays from subject to film plane, where would you draw light rays passing through the aperture? More specifically, how many different light rays could you draw? What's bad about different light rays when it comes to sharpness of an image?

 

[JSGandora]

Ahh, with small aperature comes less aberration and astigmatism right?

 

[DaveC426913]

Ahh, with small aperature comes less aberration and astigmatism right?

Well yes but it's more than that. Even with a theoretically ideal lens (no aberration or astigmatism) the effect is still there. It is not an effect of cheap lenses (otherwise the most expensive lenses would laugh at depth of field issues, would they not?)

 

[JSGandora]

Oh, because the diameter is smaller, the light rays don't really converge on a point and so some of the rays that come from the same point but pass through the hole at different points don't converge on the same point on the film which makes it blurry. Is that correct?