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What I have learned from the definition of F-number is that; The F-number (sometimes also called focal ratio, f-ratio, f-stop, or relative aperture) of a lens is the ratio of its focal length divided by the diameter of the aperture. And F-numbers are expressed as f/1, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22, f/32 etc. Hence F-number (F-stop) depends on two variables; that are diameter of aperture and focal length of the lens.

Aperture diameter/size is one of the component which governs the amount of light that enters to the camera. As far as I known, at different F-stops values (f/1, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22, f/32) the amount of light allowed to enter the camera is fixed and are with either 1/2 or 1/3 stop increment. This concept is very easy to understand, in case of prime lenses (with a fixed focal length and variable aperture), where F-stop is inversely proportional to the aperture diameter. For lower F-number (F-stop) the aperture would be bigger allowing more light and for higher Hence F-number (F-stop) the aperture would be smaller allowing less light in to the camera.

F-numbers (F-stops) have been evolved to allow a definite/fixed amount of light in to the camera (As far as I known). In case of zoom lens (with variable aperture and variable focal length), I am not able to understand the what would be the relationship between F-stop and the diameter/area of aperture at different focal length. I have two related questions

1 . In case of zoom lens, for example, Canon EF-S 18-135mm f/3.5-5.6 (with variable aperture and variable focal length). At any particular F-number(F-stop), for example at f/5.6 , does the diameter of the aperture increase with increases in the focal length? I mean, Is the diameter of the aperture at 18mm and f/5.6 would be smaller than that of at 135 mm and f/5.6?

  1. In the above case (i.e. Canon EF-S 18-135mm f/3.5-5.6 ), What is amount of light that would enter the camera at 18mm and f/5.6 compared to that of at 135 mm and f/5.6? Will the amount of lights be same or different?
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    \$\begingroup\$ Your edits have created what is materially an entirely different question, although both are based in the same incorrect understanding that the f-number is the ratio of the lens' focal length divided by the diameter of the physical aperture diaphragm rather than the diameter of the entrance pupil. \$\endgroup\$
    – Michael C
    Mar 18, 2017 at 11:00
  • \$\begingroup\$ F-numbers (F-stops) have been evolved to allow a definite/fixed amount of light into the camera No. f-numbers allow a fixed field density of light (light per unit area) to be projected on the focal plane. \$\endgroup\$
    – Michael C
    Mar 18, 2017 at 11:08
  • \$\begingroup\$ @mattdm except the accepted and other highly voted answers seem totally unaware of the difference between aperture size and entrance pupil size. In fact, the accepted answer incorrectly states that the physical diaphragm, rather than the e.p., changes size and theorizes that they do so to prevent them being f/2 lenses on the wide end! \$\endgroup\$
    – Michael C
    Mar 20, 2017 at 11:55

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Note: this answer was written to the original form of the question as asked. The question has later been edited significantly that, in effect, make it a very different question.

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The F-number of a lens is the ratio of its focal length divided by the diameter of the aperture.

F-number is actually the ratio of the focal length to the diameter of the entrance pupil. The entrance pupil is most simply defined as the apparent size and location of the aperture as viewed through the front of the lens. (Sometimes the entrance pupil is referred to as the effective aperture, but that tends to add confusion.) When a lens is zoomed to a longer focal length the magnification between the physical aperture diaphragm in the middle of the lens and the front of the lens is increased. Even though the physical diaphragm doesn't usually change size, this increase in magnification will make it appear to be larger when looking at it through the front of the lens. This is not only the case for constant aperture zoom lenses, but also for most variable aperture zoom lenses.

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At any constant F-number (while using a zoom lens), does the diameter of the aperture increase with increases in the focal length?

Not usually. With constant aperture zoom lenses the increase in magnification between the location of the physical aperture diaphragm and the front of the lens is enough to enlarge the size of the entrance pupil and maintain the f-number ratio.

What is the amount of light that would enter the camera with zoom lens at F/2.8 with 18 mm (focal length) compared to that of at F/2.8 with 50 mm (focal length)? Will it be same or different?

At 18mm and f/2.8 the entrance pupil will be about 6.43mm in diameter.
For 50mm and f/2.8 an entrance pupil about 17.9mm wide is required.

Since the light allowed to enter the lens is determined by the area of the entrance pupil, the 17.9mm entrance pupil needed for 50mm @ f/2.8 allows about 7.72X as much light to pass through as the the 6.43mm entrance pupil needed for 18mm @ f/2.8. Notice that the ratio of 18mm to 50mm (2.78) is the square root of 7.72, the ratio of the respective areas of the entrance pupils at each focal length and f/2.8.

For any doubling of focal length the entrance pupil needs to be twice as wide which will also equal four times the area to maintain the same amount of brightness. To admit twice as much light the diameter of the e.p. must increase by the square root of two, which is approximately 1.414X. The square root of two and its multiples show up quite often in photography. The standard f-stop scale is based on powers of the square root of two: 1 (√2°), 1.4 (√2¹), 2 (√2²), 2.8 (√2³), 4, 5.6, 8, etc.

In addition to constant aperture zoom lenses, let's look at variable aperture zoom lenses. Consider a 70-300mm f/4-5.6 zoom lens:

An entrance pupil of 17.5mm is needed for f/4 @ 70mm.
An entrance pupil of 53.6mm is needed for f/5.6 @ 300mm.
If the e.p. was still only 17.5mm in diameter at 300mm the aperture would be f/17!

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  • \$\begingroup\$ 2nd question answer "Not usually. With constant aperture zoom lenses the increase in magnification between the location of the physical aperture diaphragm and the front of the lens is enough to enlarge the size of the entrance pupil and maintain the f-number ratio." Can you clarify the apparent contradiction of that statement to these statements "At 18mm and f/2.8 the entrance pupil will be about 6.43mm in diameter. For 50mm and f/2.8 an entrance pupil about 17.9mm wide is required" and "For any doubling of focal length the entrance pupil needs to be twice as wide" \$\endgroup\$
    – Alaska Man
    Mar 18, 2017 at 7:59
  • \$\begingroup\$ I see no contradiction. Please explain the apparent contradiction you are seeing. \$\endgroup\$
    – Michael C
    Mar 18, 2017 at 9:38
  • \$\begingroup\$ The physical size of the aperture diaphragm is not changing. The size of the entrance pupil changes due to greater magnification of the apparent size of the aperture diaphragm as viewed through the front of the lens. The ratio of 18mm to 50mm is 1:2.78. The ratio of 6.43 to 17.9 is 1:2.78. The ratios are the same. Doubling the focal length of 18mm would be 36mm, not 50mm. Half of 50mm is 25mm, not 18mm. \$\endgroup\$
    – Michael C
    Mar 18, 2017 at 9:42
  • \$\begingroup\$ Michael. thanks for taking the time to answer. I guess i do not understand the difference between The physical size of the aperture diaphragm and The size of the entrance pupil. I thought it was contradiction because i thought a entrance pupil was the aperture opening size. And what does "apparent" size have to do with it if it does not equate to actual size. \$\endgroup\$
    – Alaska Man
    Mar 18, 2017 at 10:20
  • \$\begingroup\$ The entrance pupil is defined in the first paragraph of the answer. It is the critical measure because what light is and is not allowed to pass through the diaphragm is determined by whether it falls on the front of the lens that is included in the e.p. or not. If the e.p. is 17.9mm wide, then any light falling within that circle is refracted enough by the front parts of the lens to fit through the smaller actual physical diaphragm in the middle of the lens. It's easy to see. Just look through the front of the lens and see how the size of the aperture appears to change as you zoom in and out. \$\endgroup\$
    – Michael C
    Mar 18, 2017 at 10:26

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