# How to calculate the length of needed distance rings?

If the object distance changes by , then the image distance changes by

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

According to the Newtonian Image equation :

or shorter

A change of the object distance by results in a change of the image distance by .

As the square of the focal Length is constant:

and

which is equivalent (for z != –) to

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:

or

Say

and therefore
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:

or

Say,

and therefore
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:

or

Say,

and thus
Compared to the setting (= BFL) the image distance changes by

which is equivalent to the length of distance rings required to focus on the object distance.
This is simply, because according to Newton :

with

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:

Say,
= -5.55mm
The Back Focal Length (=BFL) increased in the 500mm position by 5.55mm compared to the setting.
How many distance rings are necessary to focus a f=50mm lens to 20cm?

According to the equation above we get:

Say,
= -16.67mm
The Back Focal Length (=BFL) increased in the 200mm position by 16.67mm compared to the setting.

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

According to the equation above we get:

Say,
= -50mm
The Back Focal Length (=BFL) increased in the 100mm position by 50.00mm compared to the setting.