(12C) Hyperfocal Distance

[Dieter]

(05-02-2018 12:55 AM)Mike (Stgt) Wrote:  

(04-30-2018 08:57 PM)Dieter Wrote:  [...] If I got the math right, the hyperfocal distance ... [...]

Which one? This wiki distinguishes two definitions of hyperfocal distance.

I refer to definition 1. Wikipedia gives the formula for the hyperfocal distance as object distance, i.e. measured from the lens' front principal plane. My formula gives the hyperfocal distance measured from the image plane, i.e. the sum of object distance and image distance, as it is common on photography. The distance scales on lenses refer to this plane. In the Wikipedia illustration this is H+x in the upper (1.) diagram. Here H is the object distance and x is the image distance.

But it is interesting to see that both established formulas have their corresponding defintions, so that one is not a simplification of the other. Instead they describe slightly different scenarios. In photography usually both definitions are considered equivalent. I have not realized this before.

(05-02-2018 12:55 AM)Mike (Stgt) Wrote:  For either formula corresponding to the definitions of hyperfocal distance I can not (or not yet) see a reason for the 3rd term (Ac) in your formula. Or is the wiki incomplete, or not so precise as I assume?

It is incomplete in that it does not give a formula for the sum of image distance and object distance, i.e. H+x.

You can derive the formula yourself: with g being the object distance and b being the image distance, b = gf/(g–f). This follows from the basic relation 1/b+1/g = 1/f. My formula calculates g+b. So simply substitute g with f²/Ac+f and there you are.

You can also get this from the Wikipedia formulas (here using A instead of N for the f-number):

Object distance:  H = f² / Ac + f
Image distance:  x = f + cf/D  =  f + cA
Distance from image plane:  H + x = f²/Ac + f + f + Ac

q.e.d.

Dieter