To stack or not to stack

Pixel Pooper wrote:

gardenersassistant wrote:

Pixel Pooper wrote:

Depth of field depends on the angle of the cones of light from the subject passing through the aperture.

Ah! Another little gem. Thank you.

The picture below shows how the aperture size and distance from the sensor determines the angle of the light cone, and how this angle affects the size of the circle of confusion and thus the DOF.

Brilliant! So simple. So obvious, seeing it like that. Thank you so much.

To keep the same magnification with double the focal length, you must double the distance to the subject, so the light cone becomes narrower unless you also double the aperture diameter, which gives you the same f-number.

So if, with the same magnification, you double the distance to the subject, you halve the effective aperture diameter? (Or the exit pupil diameter?) Thus doubling the f-number?

There is also a corresponding cone of light between the aperture and the subject. This picture makes it easy to visualise how doubling the subject distance without increasing the aperture causes the cone to narrow.

To keep the same magnification with the same angle of view, your subject distance is the same, so the light cone has the same angle at the same aperture diameter. With a smaller sensor, the same angle of view requires a shorter focal length, which gives you smaller f/number.

So the effective aperture and the angle of view change in lockstep, so you can use either in assessing the amount of/changes in DOF?

At infinity focus the entrance and exit pupil create the same angle so we can use the f/number which is the focal length divided by the entrance pupil as shown in the upper diagram below.

When we focus closer the exit pupil moves away from the sensor causing the cone to narrow which reduces the effective aperture. Imagine the exit pupil moving away from the sensor in the lower picture below and you can see how the cone becomes narrower.

The f/number is really just a simple way of expressing the angle of the cone of light. It is this angle that determines DOF, diffraction, and exposure which is why the effective aperture is the true aperture, and why for the same DOF we get the same diffraction and the same total light.

That is all very informative. You have been very helpful indeed. Thank you!