How Does One Calculate FNumber For The Longest Focal Length Of A Varifocal Lens?
The "f" in fstop actually stands for "focal length"; the format f/x is a simple radio of focal length to aperture diameter. So if your aperture is f/4 and your focal length is 10mm, your aperture diameter is 10/4, or 2.5mm.
It can make a great difference with PTZs. A PTZ may be marketed with an f/1.4 or f/1.6 lens but at the longest focal length that could be f/4 or f/5.4 etc. That will make a big difference in worse low light performance at the far / long end.
That said, most PTZs show the f stop at both sides.
1, what lens or camera are you looking at specifically?
I hate to be a negative influence but calculating the exit pupil has very little meaning in reality. The lens or camera manufacturer's specification is what has meaning. If not listed one should inquire.
That said for general information the traditional "f" stop should only be a guideline. It tells one which lens is more likely to pass more or less light to the front of the sensor.
There is another factor that lens makers no longer publish and that is the "t" stop. This is a true measurement of the light passing thru the lens. Every lens has multiple elements and each element has a light loss. The more efficient the lens ( element) design the higher percentage of light will arrive at the sensor. Thus a lower "t" stop the more light at the sensor.
As we all know the lens is only one part of the equation and the total sensitivity of the lens / camera should be a deciding factor.
The safest way to know if your camera lens will do the job in a low light situation is still to take it out to the site and try it.
I am not a "Scientist" per say but rather a person that has dealt with lenses as a camera manufacturer for many years. Why I mentioned low light is that is the area that the "f" stop becomes critical. From my knowledge the "f" stop is really the opening of the iris that allows the light to pass. It is simple on a fixed lens, but with a zoom or varifiocal all the elements loose light, therefore the lower "f" stop at the telephoto setting. I really think this may be a technical misnomer as the iris opening does not change. The "t" stop I mentioned earlier is what is really happening. The light at the rear of the lens decreases in the telephoto setting by the loss of the various lens elements. I don't believe there is a calculation that will work here as all lens designs, the efficiency of the light passage for each element, is up to the lens designer.
The only real way I have been able to determine the real "f" or 't" stop was by actually measuring the light coming out of the lens that reaches the sensor.
f/number is simply the ratio of the len's focal length to its entrance pupil diameter.
Typically, the "published" f/number is the very fastest f/number the lens is capable of, which occurs at the lowest zoom (the shortest focal length).
I hear that you want to know how to find the f/number for that same lens when it is at maximum zoom (longest focal length).
I assume that the entrance pupil is the same at all focal lengths. This may not be a 100% accurate assumption  one can imagine aspects of zooming that might change the len's entrance pupil diameter a little  but it's not likely to be way out to lunch.
With this assumption, the math falls out automatically.
entrance pupil diameter = shortest focal length / published f/number
Now that you know the entrance pupil diameter at lowest zoom, assuming diameter doesn't change much throughout the zoom, you can calculate f/number for longest zoom:
f/number = longest focal length / entrance pupil diameter
summarizing:
long focal length f/number = published f/number x longest focal length / shortest focal length
This looks a bit messy in paragraph form, so let's abbreviate:
SFL = shortest focal length
SFN = f/number at shortest focal length (the published f/number)
LFL = longest focal length
LFN = f/number at longest focal length
Summarizing,
LFN = SFN x LFL / SFL
Hope this helps.
fstop is simply the ratio of the len's focal length to its entrance pupil diameter.
Typically, the "published" fstop is the very lowest fstop the lens is capable of, which occurs at the lowest zoom (the shortest focal length).
I hear that you want to know how to find the fstop for that same lens when it is at maximum zoom (longest focal length).
I assume that the entrance pupil is the same at all focal lengths. This may not be a 100% accurate assumption  one can imagine aspects of zooming that might change the len's entrance pupil diameter a little  but it's not likely to be way out to lunch.
With this assumption, the math falls out automatically.
entrance pupil diameter = shortest focal length / published fstop
Now that you know the entrance pupil diameter at lowest zoom, assuming diameter doesn't change much throughout the zoom, you can calculate fstop for longest zoom:
fstop = longest focal length / entrance pupil diameter
summarizing:
long focal length fstop = published fstop x longest focal length / shortest focal length
This looks a bit messy in paragraph form, so let's abbreviate:
SFL = shortest focal length
SFS = fstop at shortest focal length (the published fstop for that lens)
LFL = longest focal length
LFS = fstop at longest focal length
Summarizing,
LFS = SFS x LFL / SFL
Hope this helps.
IPVM edit functions occasionally surprise, as now when it seems my edit becomes a double post.
My motivation to edit is this:
f/number can be thought of as a fraction such as 1/1.4, or as a number such as 1.4. This creates space for confusion when describing larger or smaller f/numbers.
fstops are the denominator term, e.g. 1.4 not 1/1.4.
If you assume the formula I initially provided applies to the f/number as fraction such as 1/1.4, the answer comes out wrong. If you use f/number as simply a number such as 1.4, it works as intended.
To eliminate that element of confusion, I substituted fstop for f/number.
Because of my great skill leaving messages on IPVM, that wound up as a nearly duplicate message instead of an edit.
Sorry for all the noise... Best of luck with your project.
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