I was wrong; thank you for the correction, peety3. I made at least two mistakes:

1. I should have said f-number instead of iris diameter. ("Once you've decided on a field of view, it doesn't matter how close or far away you are: there is no way to get deeper depth of field except by using a narrower f-number.")

2. Even that corrected version is inaccurate the closer you get to the hyperfocal distance. If you change your example from 10 meters to 1 meter, you will find that it is very accurate:


Depth of field, 35mm at f/4 at 1m to subject, is 122mm


Depth of field, 70mm at f/4 at 2m to subject, is 122mm


My mistake was that I didn't point out this important weakness in the approximation. Even so, I think the approximation is still very useful because a lot of photography, including the OP, is not close to hyperfocal, but I will remember to point that out in the future. While I'm at it I might point out that extreme macro can throw off the approximation as well, thanks to bellows factor.