Which aperture value determines depth of field on variable aperture lenses?

Do variable aperture values represent the way in which depth of field is rendered by a lens or only to the transmission of light (i.e the brightness)?

For example, if i wish to calculate depth of field values for an 18-50 f2.8-4 lens when used at 50mm and with the aperture set to the largest it can be (which would be f4), should i use a value of f2.8 or f4?

update: background

I had always assumed that using a 18-50 f2.8-f4 at 50mm and f4 would mean a brightness of f4 and a depth of field equivalent to using any other 50mm lens at f4, however I started to think about this after seeing two other related SE questions and answers

This question discusses how to achieve maximum DOF with the sort of lens i’m talking about, and there is a statement that the variable aperture values are actually only apparent aperture - this is from a comment by @Matt Grum

What I mean is the solid round hole in the lens through which light passes doesn't grow or shrink when you zoom, hence you're not gaining anything by zooming out and using f/3.5 The relationship between the apparent aperture and focal length (the f-stop) does change. In fact the apparent size of the aperture increases when you zoom in, meaning using the 18mm end is the worst thing you could do for bokeh

(NB I don’t feel my question is a duplicate of the question i’ve linked to because that is a discussion considering multiple variable relating to depth of field, and also the quoted text above is in a comment, not an answer)

Secondly, i know from this question that with macro lenses when focussed close the ‘effective aperture’ falls (ie they get dimmer) but depth of field doesn’t change. So consequently, i wonder if the same could be true for variable aperture zoom lenses.

If possible, I’m after an answer that explains the optics of variable aperture lenses and why they behave in the way they do

• this question has had two downvotes; perhaps i want clear enough or perhaps the answer seemed obvious. i’ve updated the question to try and make it clearer and also make it clear why the answer isn’t obvious to me and why i am curious about it. – Rich Dec 30 '17 at 11:17
• i’d also appreciate if downvoters could share with me why my question isn’t a good one - it’s something that i think is relevant to all photographers, and even if the answer is felt to be obvious i’ve searches the internet and SE and by been able to find an answer. it’s pretty dispiriting as a relative newcomer to have something immediately downvoted with no feedback as to why provided, and doesn’t encourage me to sick around and keep participating in this community – Rich Dec 30 '17 at 11:20
• the correlation of bokeh and focal length has little to do withaperture. the first question still sits there idly (use 50mm at 2.8 when it's not even possible). Also, your 18-50mm isn't a macro lens, is it? – flolilo Dec 30 '17 at 12:13
• I don’t own this lens. It’s an example (I know that fuji make one). no it isn’t a macro lens but that is an example of an instance in which the light transmitting and the depth of field producing components of a certain aperture can become de-coupled and i don’t know if that could also occur in other lenses. i’m not suggesting that i would be using a 50mm at 2.8 ‘when it isn’t even possible’, i’m simply trying to clarify my understanding of the optics of this sort of lens. thanks for describing my question as ‘idle’ - guess i’m better off keeping my curiosity to myself – Rich Dec 30 '17 at 12:22
• @flolilolilo "Only macro lenses with their 1:x-magnifications "suffer" from this aperture-deviation." Not exactly. It's just that as the magnification ratio (the ratio between size of an object in the image projected by the lens and the actual size of the object) approaches an appreciable percentage of the object it becomes more significant. Typical non-macro lenses rarely magnify more than 1:3.3 or 1:4 at MFD. Many can do no better than 1:6.7. If the MFD of such a lens were reduced even further those lenses would also demonstrate the reduced light gathering ability. – Michael C Dec 30 '17 at 22:27

The relevant measurement in terms of how lens aperture affects depth of field is not the absolute physical diameter of the aperture diaphragm, it is the diameter of the entrance pupil. The entrance pupil is the apparent size of the aperture as seen through the front of the lens.

This is true for purposes of calculating exposure. It is also true for purposes of calculating depth of field.

Constant aperture zoom lenses must have all of the changes in magnification as the lens is zoomed placed in front of the aperture diaphragm. Thus any increase in the overall magnification of the lens also results in a corresponding increase in the magnification of the aperture opening as seen through the front of the lens.

Most variable aperture lenses also do most of the changes in magnification in front of the physical aperture diaphragm as the lens is zoomed. It's just that some of that magnification is done behind the diaphragm and the size of the entrance pupil does not keep up with the change in focal length.

Take a typical 18-55mm f/3.5-5.6 lens:

• The entrance pupil diameter for 18mm @ f/3.5 is 5.14mm
• The entrance pupil diameter for 55mm @ f/5.6 is 9.82mm.
• As the magnification increases by a factor of 3.06X between 18mm and 55mm, the entrance pupil only increases by a factor of 1.91X from 5.14mm to 9.82mm.
• If the entrance pupil at 55mm were still only 5.14mm in diameter, the f-number would be f/10.7!

f/4. If the lens is marked 18-50mm f/2.8-f/4, the meaning is the widest is f/2.8 at 18 mm shortest, or f/4 at 50 mm longest. In between, widest will be in between.

Your camera ought to report the actual f/ value used in any case.

• How do you know this to be the case? I’ll update the question as to why i am wondering if the variable aperture applies to brightness only and not depth of field – Rich Dec 30 '17 at 11:08
• @Rich That's just the convention. If a lens is labelled as X-Ymm f/M-N, that means it's f/M at Xmm (widest angle, shortest focal length, widest effective aperture) and f/N at Ymm (narrowest angle, longest focal length, less wide effective aperture at full-open). If it's labelled as X-Ymm f/M, then it has an effective aperture of f/M on both ends of the zoom. – twalberg Dec 30 '17 at 14:03
• You're not answering about the DOF. – Soleil Dec 30 '17 at 18:39
• @Rich Because there's no true equivalency when using different lenses on cameras with differently sized sensors. Assuming the same shutter time and ISO, if you set up the aperture for exposure to be the same, DoF will be different. If you set up the aperture for DoF to be the same, exposure will be different. – Michael C Jan 7 at 19:16

You misunderstand the meaning of the numbers on your lens:

18-50mm clearly means it's a zoom lens. Zoom lenses come in two designs: Fixed aperture and variable aperture.

• Fixed aperture lenses are notated like 24-70mm f/2.8. The maximum aperture of 2.8 is available throughout the whole focal length range.
• Variable aperture lenses are notated like 18-50mm f/2.8-4. The maximum aperture varies with the chosen focal length: You will get f/2.8 at 18mm, but only f/4 at 50mm. The available maximum aperture changes in small ranges that are individual for each lens design: e.g. your lens could have f/2.8 from 18mm to 22mm, then f/3.2 from 23mm to 28mm, then f/3.5 from 29mm to 40mm, and finally f/4 from 41mm to 50mm.

Lens designations usually leave no clue about their minimum aperture: This one might also change over the range in variable aperture lenses.

• I understand all of these things. The thing i am uncertain about is that the aperture size determines more than one thing - it determines the brightness, and it is also has effects on depth of field. the examples i have put in my question make me uncertain as to whether, on a variable aperture lens, these two outputs always vary together on a variable aperture zoom lens – Rich Dec 30 '17 at 11:46
• @Rich Aperture is aperture is aperture. Aperture-wise, there is no difference between using a 50mm f/2.8 at f/4 and a 17-50mm f/2.8-4.0 at 50mm and f/4. – flolilo Sep 14 '18 at 9:46

As you zoom in to gain magnification, the brightness of the image projected by the lens on to film or digital sensor dims. Conversely as you zoom out and gain a wide-angle view, the brightness of the image increase. In other words, the zoom induces a focal length change and this forces the f-number to change. Since this is happening continuously, you will need to consult your camera’s information display to figure out the working focal length and the working f-number at the time of the exposure. This data comprises two the several ingredients needed to calculate depth of field. As you zoom the f-number change will be hefty. Each doubling or halving of the focal length results in a 2 f-stop change. This works out to a 4X change in image brightness.

The reason for this dimming/brighten is: The magnification change of the zoom causes the image forming light rays to spread or condense their area of coverage. Each 2X (doubling or halving) or the focal length changes the area to be covered by a factor of 4X. This fall under: “The law of the Inverse Square” (physics). In other words, zoom from 50mm to 100mm, the magnification doubles, the light fall off is 2 f-stops. The opposite, 100mm zoom to 50mm, the light gain is 2 f-stops = 4X as each f-stop is a 2X light level change.

Lens makers know that their sales will be handicapped if they don’t somehow mitigate this law of the inverse square action. One solution would be to mechanically adjust the diameter of as you zoom. This method is too complicated and too costly. A solution, allow the upfront lens elements of the zoom lens to magnify the aperture hole. This arrangement causes the apparent size of the aperture to seem to contact and expand with the zoom. This procedure actually changes the working f-number and increases or decreases the amount of light playing on film or sensor during the zoom.

If this arrangement was perfect, the lens would hold a constant f-number and thus a constant depth of filed throughout the zoom. Expensive zoom lens likely maintain a constant aperture (f-number). Sorry to report that budget kit lenses can’t maintain a constant aperture throughout the zoom. Your 18 thru 50mm zoom, starts out with a maximum aperture of f/2.8 at the wide-angle position, as you zoom in, your lens is capable to maintain this maximum aperture until you approach about 40mm, then the magnifying effect of the front element group gives up the ghost. You tipoff at f/4, that’s one stop down from your maximum aperture. In other words, your zoom loses 1 f-stop = 2X image brightness at max zoom.