How to calculate the length of needed distance rings?

If the object distance changes by \Delta z, then the image distance changes by

\Delta z' = - \frac { (ImageDistance - FocalLength) \cdot \Delta z}{(ObjectDistance - FocalLength) + \Delta z }

which is also the number of distance rings needed to refocus.

According to the Newtonian Image equation :
FocalLength^2 = (ObjectDistance - FocalLength) \cdot (ImageDistance - FocalLength)
or shorter
f^2 = z \cdot z'

A change of the object distance by \Delta z results in a change of the image distance by \Delta z' .

As the square of the focal Length is constant:

z \cdot z' = (z + \Delta z) \cdot (z' + \Delta z') = z \cdot z' + \Delta z \cdot z' + z \cdot \Delta z' + \Delta z \cdot \Delta z'
and
\Delta z' \cdot (z + \Delta z) = - z \cdot \Delta z
which is equivalent (for z != –\Delta z) to \Delta z' = - \frac { (ImageDistance - FocalLength) \cdot \Delta z}{(ObjectDistance - FocalLength) + \Delta z }

A lens with a f=50mm focal length can usually be focused from 1m. How many distance rings are required to focus it to 50cm?
The Newtonian Image Equation results in:
2500 = f^2 = (1000 - 50) \cdot z'
or
z' = \frac {2500}{950} = 2.63...
Say
\Delta z' = - \frac {2.63 \cdot -500}{950 - 500 }
and therefore
\Delta z' = 2.9.. mm
A lens of f=50mm focal length usually is focusable from 1m. How many distance Rings are required to focus it to 20cm?
The Newtonian Image Equation results in:
2500 = f^2 = (1000 - 50) \cdot z'
or
z' = \frac {2500}{950} = 2.63...
Say,
\Delta z' = - \frac {2.63 \cdot -800}{950 - 800 }
and therefore
\Delta z' = 14.03.. mm
A lens of f=50mm focal length usually is focusable from 1m. How many distance Rings are required to focus it to 10cm?
The Newton Image Equation results in:
2500 = f^2 = (1000 - 50) \cdot z'
or
z' = \frac {2500}{950} = 2.63...
Say,
\Delta z' = - \frac {2.63 \cdot -900}{950 - 900 }
and thus
\Delta z' = 47.34.. mm
Compared to the \infty setting (= BFL) the image distance changes by
\Delta z' = ImageDistance - FocalLength = -\frac {FocalLength^2}{ObjectDistance - FocalLength}
which is equivalent to the length of distance rings required to focus on the object distance.
This is simply, because according to Newton :
\Delta z' =  -\frac {FocalLength^2}{\Delta z}
with
\Delta z = ObjectDistance - FocalLength

Use the following calculator for lenses focused to infinity – for example for M12 board lenses. For “finite conjugated” factory automation lenses use the second calculator.

Use the following calculator if your lens is finite conjugated , such as for factory automation c-mount lenses.
If your lens is infinity conjugated, you might want to use the calculator above.
How many distance rings are necessary to focus an f=50mm lens to 50cm?
According to the equation above we get:
\Delta z' = ImageDistance - FocalLength = -\frac {FocalLength^2}{ObjectDistance - FocalLength}
Say,
\Delta z' = -\frac{2500}{500 - 50} =  -\frac{2500}{450} = -5.55mm
The Back Focal Length (=BFL) increased in the 500mm position by 5.55mm compared to the \infty setting.
How many distance rings are necessary to focus a f=50mm lens to 20cm?

According to the equation above we get:
\Delta z' = ImageDistance - FocalLength = -\frac {FocalLength^2}{ObjectDistance - FocalLength}
Say,
\Delta z' = -\frac{2500}{200 - 50} =  -\frac{2500}{150} = -16.67mm
The Back Focal Length (=BFL) increased in the 200mm position by 16.67mm compared to the \infty setting.

How many distance rings are necessary to focus a f=50mm lens to 10cm?

According to the equation above we get:
\Delta z' = ImageDistance - FocalLength = -\frac {FocalLength^2}{ObjectDistance - FocalLength}
Say,
\Delta z' = -\frac{2500}{100 - 50} =  -\frac{2500}{50} = -50mm
The Back Focal Length (=BFL) increased in the 100mm position by 50.00mm compared to the \infty setting.

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