This is a continuation of testing of the following macro lenses :

- Sony 90mm f/2.8 FE Macro
- Leica 100mm f/2.8 Apo Macro-Elmarit-R
- Zeiss 100mm f/2 Makro-Planar ZF
- Nikon 105mm f/2.8 Micro-Nikkor G VR

The test starts here:

The Nikon and the Sony lenses are internal focusing lenses, which means they change their focal length with distance.

I wanted to measure the change. I started out by making a big assumption: that the thin lens formula would be a reasonable approximation.

That formula is 1/i + 1/o = 1/f, where i is the distance from the center of the lens to the sensor (the image distance), o is the distance from the lenster of the lens to the object (the object distance) and f is the focal length of the lens (the distance from the center of the lens to the sensor when the lens is focused on infinity.

If r is the reduction factor (r = 1 means life size, r = 2 means half size, etc.), and d is the distance from the object to the sensor, then we know two things about o and i:

i = d – o

o = r * i

plugging those into the lens equation above and solving for f, I got:

f = d *r / (1+r)^2

So, at 1:1, f = d/4, and at 2:1, f = 2*d/9.

I set the lenses at the distance marked 1:2 on their barrels, focused on the razor blade, measured the distance from the blade to the sensor mark on the top of the camera, and this is what I got:

Then I added 1:1 for the lenses that could focus that close:

There’s something going on in the two internal focusing lenses besides just leaving the bulk of the lens alone and changing the focal length to focus. If we apply the thin lens equation to that situation, we get the focal length of the lens to be:

f = r * F / (1+r)

where F is the focal length at infinity, and r is the reduction ratio as defined above. For r = 2, the above equation evaluates to 2*F/3, which would say that the 90mm Sony would be a 60mm lens at 1:2. It is actually more like a 78mm lens.

David Braddon-Mitchell says

Right!

I had done back of the envelopes using tlf on what I should expect with a fully IF 90mm when I got my Sony, and was surprised (and pleased) that it seemed to give slightly more working distance than I expected…

The other thing, which I have not measured or really tested, is that focus stacking using exposures adjusted with the ring rather than the rail (just the smallest amount I can manage) seem to align a bit better than I feared with IF..