Is the size of the entrance pupil the same as the size of the effective aperture?

I understand that the entrance pupil is the image of the aperture as seen from the front of the lens. However, is the size of the entrance pupil the same as the size of the effective aperture? In other words, if I measure the size of the entrance pupil by looking at it, will that be equivalent to the focal length of the lens divided by the f-number (with the focus set to infinity)? I know that sometimes this is hard to estimate because of the shape of the aperture blades, but I was wondering whether pupil and aperture can be quite different (perhaps at very low magnification).

if I measure the size of the entrance pupil by looking at it, will that be equivalent to the focal length of the lens divided by the f-number

Yes. F-number is defined in terms of focal length and entrance pupil diameter, so if you know any two of: entrance pupil diameter, f-number, and focal length, you can calculate the third number.

The equation that Wikipedia gives is:

N = f/D


where N is f-number, f is focal length, and D is entrance pupil diameter. Dividing both sides by f and taking the reciprocal of both sides gives you:

D = f/N


Note this sentence from the linked article:

The entrance pupil diameter is not necessarily equal to the aperture stop diameter, because of the magnifying effect of lens elements in front of the aperture.

• I was under the impression that the f-number was defined as the ratio of focal length and aperture, and that the entrance pupil was just the apparent size of the aperture. I tend not to necessary trust wikipedia. Here for example (en.wikipedia.org/wiki/Aperture) the f-number is specified as a ratio of "focal length to effective aperture diameter". Oct 16, 2013 at 15:27
• @ maupertius -- At the bottom of that Wikipedia article is a list of topics. Click on "Numerical aperture versus f-number", that referral will clarify. Mar 23, 2019 at 15:35

Entrance pupil (EP) is the more commonly accepted technical term. Effective aperture (EA) means the same thing when referring to the aperture opening used to divide the focal length by to figure the f-number. But EA is less accepted in technical circles because it is less specific in some other ways. It gets confusing because when we say we are choosing an aperture setting of, say f/5.6, what we are really doing is selecting an f-number of 5.6. The effective aperture we choose to get a specific f-number, such as 5.6, will vary based on the focal length of the lens. A 100mm lens set at f/5.6 will have an entrance pupil/effective aperture 17.86mm wide. A 17mm lens set at f/5.6 will have an EP/EA only 3.04mm wide.

The width of the EP is affected by the magnification provided by the lens elements between the physical aperture diaphragm and the front of the lens. That is how a constant aperture zoom lens works: the magnification increases the size of the EP at the same rate of increase as the increase in focal length, even though the physical size of the diaphragm does not change.

Or, to put it another way, Effective Aperture (EA) is the apparent width/diameter of the Entrance Pupil (EP) as measured from outside the front element of the lens. But the EP also has additional properties beyond the EA. And Wikipedia is correct at this point: The width/diameter of the EP is always used to calculate the f-number of a lens.

If you have a non-circular opening, for example, you would need to measure the total area of the oddly shaped EP and then use the diameter of a circle that would yield the same area when dividing the focal length to derive the f-number, for purposes of exposure calculation, of such a lens.