Using tiny apertures - Part 7, the apertures are definitely not so tiny

 In this post I mentioned the uncertainty over what f-numbers I am actually using ("effective apertures") when I am setting tiny apertures (large f-numbers) on the camera/lens.

It seems that my modified formula is giving the correct answers. I'll explain here in terms that I can understand. If you want to know more about the technical/optical factors in play please refer to this thread at dpreview.com, particularly the posts by alanr0.

I have been testing the formula 

effective f-number = nominal f-number * 

                 ( 1 + magnification/ (pupil magnification * teleconverter power )  )

I have been using it with the assumption that pupil magnification is 1 (because I don't know what it actually is, and 1 is a sensible value to assume and seems to work fine). So with this assumption the formula becomes 

effective f-number = nominal f-number * 

                 ( 1 + magnification/ teleconverter power  )

However, I have been using magnification so as to include both the magnification provided by the lens and also the magnification provided by the teleconverters. So 

magnification = Lens magnification * Teleconverter power

This means that magnification/teleconverter power can be written as 

Lens magnification * Teleconverter power / Teleconverter power, 

which is simply Lens magnification.

This means that my formula can be written as

effective f-number = nominal f-number * ( 1 + Lens magnification )

This is true only if nominal f-number is the f-number set on the lens adjusted to take account of any teleconversion being used. So for example minimum aperture of f/2.8 when using a lens without a teleconverter becomes minimum aperture of f/5.6 when a 2X teleconverter is used. This is how my setups report f-numbers when I'm using teleconverters.

This formula gives exactly the same answers as the modified formula I used in the previous post, and these answers match the practical results of the test exercises I have been doing.

This means that, for example, when I use f/45 with 8X magnification, using a pair of 2X teleconverters, the effective aperture is around f/135 rather than around f/400 as I previously thought.