In an effort to win a bet with a friend, who can name the stops between: f2.8 f4 f5.6 f8 f11 f16 f22 (ie. what is the stop between f16 and f22)

If you want to nitpick, the half-stops are 3.4 4.8 6.7 9.5 13 19 etc to two significant figures. Suppose you want nth stops (ie n=2 for half stops and n=3 for third stops), then the ratio between the stops is 2^(1/(2*n)). Start at an exact f-stop (ie 0.5, 1, 2, 4, 8, 16, 32 etc) not the rounded-off stops (ie 0.71, 1.4, 2.8. 5.6. 11, 22 etc). The ratio for half stops is 1.189207 to seven sig figs. Best, Helen PS Who wins the bet?

But for a 250mm Soligor telephoto lens, what would be the diameter of the aperture opening at f11? Think ya know?

No. You've got me there. I don't know how to tell the diameter of the physical aperture opening from only the focal length and the maximum f-stop. Best, Helen

lol lol lol @david. and thanks for helen and her math skills. Sometimes half stops are mind bending let along 1/3rds.

Guess what, there's one on eBay right now. I thought the trick in the question was that the f-number is calculated from the diameter of the entrance pupil, not the diameter of the aperture. Best, Helen

Now how can I be expected to know what I meant? But, ahem, maybe I wrote 'seven sig[nificant] fig[ure]s', not places. Best, Helen

The trick is knowning what the entrance pupil is and how large it is... (lets not get into pupil coma)

Hi ! IIRC from my long ago optic classes, the F stop diameter is got from the exit pupil diameter of the lens. the writing f:2.8 means that the focal lenght (here near 250 mm) is divided by 2.8 to get the exact pupil diameter. But, on a telephoto lens, the size of the hole delimited by the aperture blades is magnified by the lenses between it and the film. So it is difficult to calculate the size of the hole given the measured exit pupil size. Do I make myself clear ??? If you own a large format lens, of telephoto design (or wide angle disgn , thins are reversed but same reasonning apply) you can using a ruler measure the size of the pupil, remove the rear lens element and measure the hole diameter... Be carefull, lenses and blades are easilly damaged. Have a nice day !

Oh, I forgot ... You said that the lens is engraved 250 mm focal length. This is not true. If you measure YOUR lens focal lenght, you'll see it is a bit more or a bit less than 250 mm. This is due in tolerance in calculation and in making the lens. Of course, this will impact the calculation of the F stop opening diameter... Have fun !

I've heard of EXIT pupils. They are to be considered when purchasing binoculars. Entrance pupils are a new one on me. Dan

No, the F-stop is from the entrance pupil. When doing close-up work the exit pupil becomes important for calculating exposure compensation, but not for calculating the F-stop (or indeed DoF). The designation "telephoto" is often misused to mean any lens longer than "normal". They are not necessarily telephoto lenses even if they're long - my 135mm Hector is a "normal" lens in a long barrel. I don't know whether the Soligor is a long lens or a telephoto lens, though...

To calculate the diameter of any 250mm lens at f/11. You divide 250 by not 11 but by 11.3137... and get 22.9708691. Remember only the " even" stops are exact. Even stops include 1, 2, 4. 8, 16, 32, 64... the "odd" stops are either the next higher or lower stop divided or multiplied by square root of 2 as the case may be.