Why does a zoom lens seem to lose focal length at close focus, and how can I estimate its field of view?

Question

My Nikon 28-300mm can focus very close, but at short distances its framing is much wider than I expected. For example, compared with a 105mm macro lens plus 2x teleconverter, the 28-300mm at 300mm gives a noticeably wider field of view at close range. I’ve read that this is due to internal focusing and that the lens’s effective focal length becomes much shorter near minimum focus.

What optical principle causes this? Why can a lens marked 300mm behave more like a much shorter lens at close distances?

Also, if maximum magnification and minimum focus distance imply an effective focal length at minimum focus, is there a way to estimate the effective field of view or focal length at other subject distances, such as 300mm at 3m? Can this be calculated from specifications, or does it usually require measurement?

user1375 · Accepted Answer

The principle of physics behind this behaviour is nothing more than the thin lens formula:

1/o + 1/i = 1/f

Where o is the object distance (distance from lens to subject), i is the image distance (distance from lens to sensor), and f is the focal length.

For a very large object distance (approaching infinity) the 1/o term drops to zero, hence:

1/i = 1/f
i = f

This means a simple 300mm lens will form a focussed image of a very very far away object a distance of about 300mm behind the lens. This means if it is mounted in tube which places the lens 300mm from the sensor then you will get sharply focussed photographs of objects on the horizon.

What about an object close to the lens at a distance of 600mm?

1/600 + 1/i = 1/300
1/i = 1/600
i = 600

The same 300mm lens mounted in a 300mm tube will produces images of objects at this distance which are completely out of focus, however if we lengthen the tube to 600mm our close up object is brought into sharp focus.

We have created a "unit focussing" lens. The problem with such lenses is that they massively increase in physical length when focussing.

To avoid such a huge change in physical length in a close focussing lens like the 28-300mm, designers employ "rear focussing" which works by varying the focal length when focussing close. Going back to the thin lens formula, if a 300mm lens mounted at a fixed distance changes to a 100mm lens, focus changes from infinity to:

1/o + 1/300 = 1/100
1/o = 1/150
o = 150

One hundred and fifty millimetres (which is pretty darn close!).

You can in theory use the same formulas to work out the relative focal lengths at different focus distances, but with the caveat that in a complex multi-element lens the distance o corresponds to the object distance from the front principal plane and the distance i corresponds to the image distance from the rear principal plane. The location of these planes depends on the lens design and is not frequently specified by the manufacturer.

Ultimately rear focus makes it relatively easy to drop the minimum focus distance down, which allows manufacturers to slap "macro" on the description and sell more lenses, but as focal lengths are by convention always stated with the lens at infinity focus the customer is in the dark about what's actually happening. All you can really do is treat stated focal length and aperture values as approximate values for moderate focus distances only.

Why does a zoom lens seem to lose focal length at close focus, and how can I estimate its field of view?

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