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Re: [OM] 65-200mm or 200mm and Extension Tubes

Subject: Re: [OM] 65-200mm or 200mm and Extension Tubes
From: frieder.faig@xxxxxxxxxxxxxxxxxxxxxxxxx
Date: Mon, 30 Oct 2000 23:57:34 +0100
On Mon, Oct 30, 2000 at 08:09:43AM -0600, Franklin A. Berryman wrote:
> Thanks for the very lucid explanation.  So a 90mm f2.0 Zuiko which goes to 1:2
> has 45mm extension (45mm/90mm), with a 25mm extension tube its go to 1:1.3
> (45mm+25mm/90mm), and with a 65-116 variable extension tube, it goes from
> 1.2:1 (65mm+45mm/90mm) to 1.8:1 (116mm+45mm/90mm).  Now, how do I figure out
> the magnification ratios for the regular lenses from 135mm up.  The sales info
> only give close focusing distances?
> 

This is not too easy to calculate. It is necessary to iterate
 or you`ve to solve quadratic equation.
 In a book I found  the following instructions to calculate 
the extension for a lens for a given focusing Distance (FD):

1.) The needed formulas are based on this two equations:

FD = z + 2*f + zs       [1]
f^2 = z * zs            [2]

Explanation:
 FD - focusing distance: Film plane -> Object
 f  - Focal length of lens
 zs - extension of the lens, The value you want.
 z  - distance object -> 1x focal length before lens ´regard as just a value´

1. Iteration assume zs -> 0 :

 Calculation of z with [1]: z= FD - 2*f  is the first value for z called z_1 
for now.
 Calculation of zs with [2]: zs_1 = f^2/z_1

2. Iteration calculate a more accurate z value with zs_1:
 
z_2 = FD - 2*f -zs_1
zs_2 = f^2/z_2

3 .... and so on.....

With evera iteration you`ll get a more accurate value for the lens extension.
With this value you can determine the magnification ratio.....
 m =  zs / f

Hmm, now here a calculation for 200mm and FD =2500mm : 

1. Iteration:
z_1 = 2500 - 2* 200 = 2100
zs_1 = 200^2 /2100 = 19.047...
2. Iteration: 
z_2 = 2500 - 2*200- 19.047 = 2080.95...
zs_2 = 200^2 / 2080.95 = 19.22....

I think this is accurate enough.... you can try another Iteration when you want.
Now the magnification would be:

m =  19.22 / 200 = 0.096..

This calculation is not too nice, but works.

Frieder Faig

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