[photo-3d] Re: Loupe question, magnifiers, confusion

[zilch0@xxxxxxxxxxxx]

--- In photo-3d@xxxxxxxxxxx, Paul Talbot <ptww@xxxx> wrote:

> If viewer lenses are in the "lens" category, how is their
> magnification calculated?  In several years of reading a few
> different 3D lists, the only magnification formulae I've seen
> are the 250/fl you mention, and 250/fl + 1.  What is the
> reasoning for the +1?
> 
> Paul Talbot

I came across an answer to this question some time ago, when
searching the net for information about loupes, but I've only just 
tonight read your post.  I can't remember the source for what I'm 
about to quote, but I made a spreadsheet using the data I found so
I'm quite certain this is correct (at least it's a match to the 
unidentifed source!)  

It turns out that the magnification offered by a lens varies with the 
close focusing abilities of the user.  For most people with good 
vision, the closest they can focus on a subject, with their bare
eyes, is 10 inches.  For these people, a given loupe (or stereo 
viewer) is said to have a maximum magnification equal to:

   Magnification = 250mm/FL + 1

  (Where FL is the focal length of the lens.)

We've all seen this forumla...

Some strongly nearsighted people, can easily focus as close as 5 
inches.  For these people, that same loupe or viewer lens, would be 
said to have a maximum magnification equal to:

   Magnification = 250mm/FL + 2

The closer you can focus, the higher the magnfication!!

And for a farsighted person who can't focus any closer than 20
inches, the formula would be:

   Magnification = 250mm/FL + 0.5

This relationship, between magnification and the closest focus 
achievable by a given user, adheres to this formula (which I 
determined empirically using the above data):

   Magnification = 250mm/FL + (10 * x**-1)

   (That last bit is "Ten times x to the minus 1".)

   Where x is the closest focus distance achievable, in inches

For example, when x = 10 inches:

   Magnification = 250/FL + (10 * 10**-1) 

which reduces to:

   Magnification = 250/FL + 1

Another example, when x = 12 inches (like it is for my eyes):

   Magnification = 250/FL + (10 * 12**-1) 

   Magnification = 250/FL + 0.833  

I don't enjoy quite as much magnfication as someone who can focus at 
10 inches.

If we could focus on an object at 0 inches distance, the formula
would describe the intrinsic magnfication offered by the lens itself:

   Magnification = 250/FL + (10 * 0**-1)

   Magnification = 250/FL + 0   

We've seen this formula, too!


Summary:

To determine the magnfication of a lens, use:

   Magnification = 250mm/FL + (10 * x**-1)

Where x is the closest focus distance the user can achieve WITHOUT 
the lens, in inches.

There you go!
    
Mike Davis