# How can I calculate magnification ratio I get by reversing a lens?

I am looking for a way to mathematically determine the maximum magnification ratio that is possible/practical to achieve by reverse mounting a non-macro lens, prior to purchasing the lens.

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• Wouldn't this require some type of value to be assigned to the reversing hardware? I don't recall seeing anything like that on any that I own. – dpollitt Jan 3 '12 at 21:14
• If the reversing hardware contains no optical elements, shouldn't it have little to no effect on anything other than the focus plane? – Sean Jan 3 '12 at 21:16

The magnification will indeed depend on your reversing hardware. The more distance you put between the lens and the body, the higher the magnification. The exact formula is:

``````magnification = lens_to_sensor_distance / focal_length - 1
``````

The problem is that the distance from the lens to the sensor has to be measured from the relevant principal plane of the lens, i.e. the object side principal plane, which becomes image-side once the lens is reversed. Then, to compute the magnification, you need to know the position of this plane inside the lens. Alas, I have never seen this information published for current lenses. You may be able to compute this position yourself... provided you have the complete formula of the lens! Finding the necessary data may be harder that finding someone you could borrow the lens from to do an actual test.

As for the question of what is practical... assuming you can achieve unlimited magnification (bellows, etc...) you will likely be limited by the resolution getting bad at too high magnifications. You can expect the MTF50 of the lens to be roughly divided by the magnification. Then the maximum practical magnification will be:

``````max_magnification = lens_resolution / required_resolution
``````

I'm afraid you cannot determine that magnification ratio mathematically.

Peter Forsell's great Math for macro photographers page contains lots of macro magnification ratio calculations for different scenarios, but in the section about the reversed lens, he claims the following:

We cannot directly calculate the zero extension magnification (Zm) of the lens we wish to mount in a reverse position. Instead we have to take a test photograph of a ruler to determine this value or find the information in the lens manual.