Sk Apo-Digitar 80/6.7 (80Ad)

To see the full resolution images, you need to go to my photobucket page and download the images manually. This is apparently a new feature for Photobucket beta, ie anyone, not just the owner, can access full-resolution images. Here's he link to the page with the images:

http://s943.beta.photobucket.com/us...ARD1%20105PN

I'm not sure of list price, but I paid $100 for it on ebay. Not cheap, but not outrageous. The fixed f6.7 is easier to work with for Cents (no stacking) than the f4 of the fixed 75ARD1's. Keep in mind these shots are all at f6.7, so the 75ARD1 and especially the 105PN are not at their best. But if you are going to shoot at f6.7 for good DOF then the 80AD is essentially equivalent to the 75ARD1.

Hmm, to me the 75ARD1 is a tad sharper near the edge, with the 80AD showing what I would interpret as a small amount of halation. Maybe there's a slight difference in where the two lenses were focused? Regardless, it comes very close to the 75ARD1 which is no mean feat (although I like to use that lens at f/5.6 where it performs a bit better). Of course, the PN is ridiculous.

For $100 it it does represent a nice alternative to the 75ARD1 for someone who wants a little step up from an el-cheapo.

If we want to get more specific, that effective aperture formula is correct (or close enough) for lenses with a pupil ratio of 1 (the 75ARD1 is symmetric, and has that property). For lenses with a different pupil ratio, the formula is more complicated and it might be hard to find out what the pupil ratio is for a given lens (or it could even be variable - likely the case in a lens which changes focal length like the Canon 100mm macros).

The simple formula could be only approximate, or it could be significantly wrong, and I don't understand all the math, so take all that stuff with a grain of salt. It generally works as a first-order approximation, and knowing the exact number is usually not important.

For microscope objectives, the formula to convert Numerical Aperture (NA) to a familiar infinity f-number is:

Infinity Aperture = 1/(2*NA) * MAG/(MAG+1)

The MAG+1 cancels out with the same component in the previous equation, so MAG/(2*NA) is the effective aperture for a microscope objective operating at its rated magnification. A common 4x/0.1 would therefore the rough equivalent of an f/4 lens. A 10x/0.25 is something like f/1.8. At high magnifications the MAG/(MAG+1) factor is close to 1 and so you frequently see the formula without it. The other caveats and addendums for that formula are beyond my ken.

Generally only macro people care about effective aperture and it's easier to just communicate the nominal/infinity f-number and magnification. For everyday photography of common macroscopic objects (e.g. a LOLCat), even at distances much closer than "infinity" the magnification is so low that it can be ignored. A typical domestic Felis catus lolrus of 60cm length more than fills the sensor at 0.04x, so the MAG+1 factor almost disappears. The effect is 1/3 of a stop (the smallest exposure step on most cameras) at 0.12x and a full stop at 0.41x (a half dollar fills an APS-C sensor at about 0.46x).