how many f stops should I allow for a given change in focal length - ISO and shutter speed remaining constant?

Question

There are charts that show me what how many stops in shutter speed or ISO to allow when, for example, using an ND filter but given that a longer focal length reduces light available is there a chart to tell me what allowance in F stop to make for a change in focal length? I'm not a mathematician nor a physicist so explaining the reasons or calculations doesn't help me. That would be like asking somone the time and being told how a watch works. Straight question - does such a table exist or not and, if so, where can I find one?

Answer 1

MC's answer points out how the fstop comes to be. But, how does it affect light?

Let's take the first example of a 70-200 f/2.8 lens. At 70mm, the entrance pupil is 25mm in diameter, while at 200mm it is 71.5mm in diameter. (I know you said no math, but bear with me).

The ratio between 70 and 25 is 2.8 while the ratio between 200 and 71.5 is...also 2.8!.

The lens is designed so that, in order to compensate for the light loss effects of increasing focal length, a wider entrance pupil is used. The beauty of this and of using the fstop system is that we don't have more math to do - we can simply calculate exposure based on f/2.8 while at 70mm or at 200mm and know that it's the same amount of light.

Answer 2

The f-number is a ratio between the focal length and the diameter of the entrance pupil. As a ratio, it is a dimensionless number. Simply put, the entrance pupil is the size the aperture appears to be when viewed through the front of the lens.

For a constant aperture zoom lens, the entrance pupil size enlarges at the same rate as the focal length increases. This is due to the changes in magnification between the front of the lens and the physical aperture diaphragm as the lens is zoomed. For example, for a 70-200mm f/2.8 lens, the same wide open diaphragm appears to be 25mm in diameter at 70mm focal length and appears to be 71.5mm in diameter at 200mm focal length.

For variable aperture zoom lenses, the magnification still affects the f-number. But the increase in size of the entrance pupil does not quite keep up with the increase in focal length, usually because some of that increase in magnification occurs in the parts of the lens behind the physical aperture diaphragm.

Take for example a 70-300mm f/4-5.6 zoom lens.

• At 70mm and f/4, the entrance pupil is 17.5mm in diameter.
• At 300mm and f/5.6, the entrance pupil is 53.6mm in diameter.
• To maintain f/4 at 300mm, the entrance pupil would need to be 75mm across.
• If the entrance pupil were still 17.5mm in diameter at 300mm, that would result in an f-number of f/17!

Since each zoom lens design is different and the amount of magnification occuring in front of the aperture diaphragm and behind the aperture diaphragm can vary from one design to the next, each variable aperture lens has its own characteristics with regard to the maximum f-number at any particular focal length.

Answer 3

The focal length of a lens expresses its power. Short lenses yield tiny images of objects, whereas long lenses return magnified views. We label short lenses “wide-angle” and long lenses “telephoto”. In-between, we brand the power of the lens as “normal”. When you zoom your camera lens, you are changing the focal length.

It’s true, as you zoom, the brightness of the image projected by the lens on to the image sensor, at the rear of the camera, changes. Each time you double the focal length, image brightness drops to ¼ of its original brilliance. Conversely, if you zoom, reducing the focal length by ½, image brightness raises four fold. Thus, focal length changes induce immense changes in image brightness. This is actually a big problem. If action is not somehow taken, this change in image brightness is catastrophic. Catastrophic, in this incident means severe under or over exposure.

Before you get all excited, you need to know that photographers have faced this problem for a century and a half. Thus, one way or another, the problem has been solved for you, so you can relax. In other words, unless you are working with the simplest of lenses and cameras, you need not pay much attention to these facts of physics.

How the photo community copes: The amount of light from a vista that is projected on to the image sensor is a function of the focal length of the lens and its working diameter. We divide the focal length by the working diameter and the resulting value is called the focal ratio. The happy news is, within reason, any lens set to the same focal ratio as another, presents the same image brightness to the image sensor. In other words a giant camera set to the same focal ratio as a miniature camera, delivers the same image brightness. We abbreviate focal ratio as f-number or f/# or f-stop etc.

Modern zoom lenses have a trick up their sleeves that keeps the image brightness constant. The front lens element group of the zoom lens moves towards or away from the lens stop as you zoom. The lens stop is a circular entrance of the lens. This opening, also called an aperture, is mechanically adjustable as to its diameter. You or your cameras automation set this diameter (f-number) based mainly on scene brightness. If correctly set, the image brightness playing on the image sensor, together with the shutter speed and ISO setting, deliver a satisfactory exposure. Once set, as you zoom, the view of this entry way is magnified by the front lens group. This magnified view is a variable based on the spacing of lens to stop. High end (expensive) zoom lenses maintain a constant f-number, thus constant image brightness throughout the zoom. Less expensive zoom lenses give up the ghost near maximum zoom. In other words, they fail to keep a content exposure. But wait, this is not horrific; the modern camera reads the exposure change and compensates wholly.

Bottom line, you don’t need a table of focal length to exposure compensation unless doing scientific or critical work with simple cameras and lenses.

Answer 4

I'm not a mathematician nor a physicist so explaining the reasons or calculations doesn't help me. That would be like asking somone the time and being told how a watch works. Straight question - does such a table exist or not and, if so, where can I find one?

This is totally understandable, but the problem really is that you're over-thinking it. There is no table, because the f/number values are actually the pre-computed thing you need. To extend your analogy, you are looking at a watch and saying "How can I tell time when I don't know the ratio of gears to the oscillator crystal's cycle?" You don't — you just look at the hands.

People are explaining the reasons and calculations in order to lead you to this conclusion, but the simple answer is that the table would like this:

focal length | pupil diameter | f-stop | exposure value at ¹⁄₆₀th

    50mm     |     25mm       |  f/2   |     8
   100mm     |     50mm       |  f/2   |     8
   200mm     |    100mm       |  f/2   |     8
   400mm     |    200mm       |  f/2   |     8

    50mm     |     12.5mm     |  f/4   |    10
   100mm     |     25mm       |  f/4   |    10
   200mm     |     50mm       |  f/4   |    10
   400mm     |    100mm       |  f/4   |    10

    50mm     |      6.2mm     |  f/8   |    12
   100mm     |     12.5mm     |  f/8   |    12
   200mm     |     25mm       |  f/8   |    12
   400mm     |     50mm       |  f/8   |    12

... and since we don't work with the effective pupil diameter, just with f/stops, you don't need it at all.

For more background on all of this, see:

• Why are the area of aperture, focal length, and amount of light specified in these terms?
• What does f-stop mean?
• Why doesn't exposure change when changing focal length?
• What is the EV scale?
• What is one "stop"?