Frank Wajer <[EMAIL PROTECTED]> writes:

> from lens FAQ
> <snip>
> Q10.  What are the closest and farthest points that will be in
> acceptably sharp focus?
> 
> A.  Sclose = h * So / (h + (So - f))
>     Sfar   = h * So / (h - (So - f))
> 
> or, defining hr = h/(So - f)
> 
>     Sclose = So * hr/(hr+1)
>     Sfar   = So * hr/(hr-1)
> 
> Think of hr as the hyperfocal to subject distance ratio.  These
> formulas are also correct when hr is defined as hr = h/So and the N
> used in computing h is actually Ne.
> <snip>
> 
> I think the last paragraph is wrong. Can anyone comment?

I agree with you, this statement about an alternative definition for hr
is indeed incorrect.  One can see this either by directly substituting
the definitions for the various variables, or with the following
argument:

(1) hr = h/(So - f)  and h = f^2/(N*c)  

(2) hr = h'/So      and h' = f^2/(Ne*c)

[notation as in lens FAQ
<URL:http://www.photo.net/photo/optics/lensFAQ.html> or lens tutorial
<URL:http://www.photo.net/photo/optics/lensTutorial.html>] 

Now the effective aperture Ne is always larger than or equal to the
aperture N, so h' is always smaller than or equal to h.  Also So is
always larger than (So - f).  Therefore the hr in the second definition
is always smaller than the hr in the first definition.

How did you come across this problem?

cheerio
ralf

-- 
Ralf Stubner <mailto:[EMAIL PROTECTED]>

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