closest point on optical axis with an image that has „acceptable sharpness“
Where CoC is the Circle of Confusion (the largest accepted Airy-disk) in Millimeter.
Alternatively, we can express the NearPoint using the magnification M :


A 5 Mega lens with f=7.2mm focal length and F-stop F2.4, focused to an object distance of 100mm then has a far point of

und einen Nahpunkt von

and thus



A 5 Mega lens with f=7.2mm focal length and F-stop F2.4, focussed to 100mm then results in

and a nearpoint of

thus we get




see also https://www.optowiki.info/blog/can-i-increase-the-dof-by-changing-the-focal-length/


The DOF is

Yet another way to express the Near-Point is to use the Hyperfocal distance H :
If the lens is then focused to some object distance OD, this OD can be expressed as fraction of H :
or
Then the near point is
,
the far point is
and the Depth of field is

Therefore from

we get

This means however, that

and therefore,


For we get
So, with
and
we get
For we get
So, with
and
we get
Therefore by decreasing the OD by factor 2, the DOF decreased by factor 4.
or, equivalent :