I think I need a little more help but I will get it.
Let's say we have converging lens of focal length f= 1 cm.
An object is placed at distance d_o. The image is located at distance d_i (calculated using the lens equation). The images at all other planes are blurred (circle of confusion for each image point).
The depth of field DOF depends on the distance d_o. I understand what they conceptually are: axial distance over which the circle of confusion size is small enough to make the images acceptable.
Now, "optical infinity" starts where? At roughly 20, 30 times the focal lengths (I hear). So infinity could be 100 cm away. Everything farther than that considered to be at infinity....
What is the DOF if the object is at infinity? Is it small or large?
The hyperfocal length that distance H. If we focus at H, everything from H/2 to infinity will be in (acceptable focus). Perfect focus will be at H. All the other image planes will be slightly blurred.
Focusing at H give twice the DOF than focusing at infinity.
But regardless of where we focus, of where the object is, the circle of confusion size grows as we move away from the perfect focus plane. If we focus at H, how can things that are way far from H, at infinity, still be in acceptable focus? Wouldn't the size of hte circle of confusion be so large at that distance?