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I guess this is more a question of optics than photography but I just got an SLR with a basic 18-55 lens. I noticed that when going from 18 to 55 or 55 to 18 the lens physically comes back in and then physically goes back out?

What is going on there? I would think that if I am zooming in the lens should be going out 100% of the time but the lens actually goes out and then comes back in.

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@mattdm Both of the existing answers are correct -- it depends on the lens. That's why both seem plausible. A zoom that has a shorter focal length at any point than the flange-to-sensor distance must be retrofocal. By the same token, if the optical center is closer to the center than the apparent focal length at any point, it must be telephoto. Some lenses are both, depending on the focal length setting. The Nikon 18-200 must be retro at 18mm, but is only 162mm long fully extended. Add the flange distance, then account for the location of the optical center of the lens: it's telephoto. QED –  user2719 Dec 28 '11 at 21:08
    
Could you please take the lens out of the body, look at the rearmost element, and tell us how it moves when you zoom from 18 to 55 mm? –  Edgar Bonet Dec 28 '11 at 23:26
    
As I understand DragonLord's answer, the explanation is that retrofocal lenses increase in extension as they zoom out, and telephoto lenses increase in extension as they zoom in, and that this type of lens crosses between the two. Edgar Bonet's answer says that this "switchover" of direction of lens extension happens even with completely retrofocal designs, and that if the lens happens to also be telephoto when zoomed in far enough, that's incidental. Which of these is true? –  mattdm Dec 29 '11 at 14:20
    
@EdgarBonet -- the movement of the rear and front) element alone is not sufficient to make a determination either way for a particular lens; you'd need to take the lens down to groups and helicoids to be sure if the design isn't published. –  user2719 Dec 29 '11 at 16:29
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@Zach: can you un-accept DragonLord's answer as per his request? See below.... –  mattdm Dec 31 '11 at 20:48

3 Answers 3

up vote 26 down vote accepted
+100

There is no simple relationship between the physical length of the lens and its focal length. For example, a retrofocus wide angle is generally longer than its focal length, while a telephoto lens is shorter than its focal length. Inside a zoom, you have several lens groups that move independently. The focal length of the zoom depends on the relative positions of the groups, and is not always simply related to the physical length of the lens. That being said, the simplest possible explanation for this behavior is that your zoom may be of a simple retrofocus design.

Retrofocus zoom

A retrofocus zoom is made of only two groups. The front group, of negative refractive power and (negative) focal distance f1, makes a virtual intermediate image of the object somewhere in front of the lens. This group works much like the glasses short-sighted people wear: it brings the object “closer to the eye”. The focal length of this group is close to -35 mm.

The rear group, of positive refractive power, makes on the sensor an inverted real image of this intermediate virtual image. The intermediate image is the “object” for this group. The final image is like an inverted copy of the virtual image, scaled by a magnification factor m2 close to -1, which is negative because the final image is inverted.

Assuming the object is at infinity, the whole lens has a focal length f = f1×m2. This is a product of two negative numbers, and the result is positive.

retrofocus lens

In the above simplified drawing, the first group is the lens L1, the second group is the lens L2, the zoom is focused at infinity, the intermediate image is at the left, at a distance x from L2, and the sensor is at P. The magnification of L2 is m2=-x’/x.

With this design, it is easy to zoom the lens by moving the second group. When this group is closer to the sensor, it provides a small magnification (say around -0.5) and thus a shorter focal length for the whole lens. When it is moved forward, closer to the intermediate image, you have higher magnification (say around -1.6) and thus a longer focal length for the whole lens.

However, as you change the magnification of this group, the distance between the object (in this case the intermediate image) and the final image changes. This distance is at a minimum when the group is just in between its object and its image, which happens when the magnification is -1. You can check this easily by using a magnifying glass to focus the image of a lightbulb on a piece of paper: the distance between the the bulb and the focused image is minimal when the image has the same size as the object. In the case of the zoom lens, since the final image has to fall at a fixed position (on the sensor), the intermediate image has to be moved by moving the front group. This explains the observed behavior of the front group: as you zoom the lens from 18 mm to ~35 mm, the magnification m2 goes from ~-0.5 to -1 and the front group moves closer to the sensor. As you zoom from there to 55 mm, m2 goes from -1 to ~-1.6 and the front group moves away from the sensor.

Example 1

This is just a theoretical (over)simplified model for a zoom where each group is just a thin lens. The focal lengths of the groups are -35 mm (front group) and +35 mm (rear group). Assuming an object at infinity, I calculated the configurations of the zoom for three focal lengths. The table below shows the positions of the lens elements (in mm from the sensor) as a function of the focal length the zoom is set to:

┌───────────┬─────────┬─────────┐
│ f. length │ group 1 │ group 2 │
├───────────┼─────────┼─────────┤
│   18 mm   │  121.1  │    53   │
│   35 mm   │  105    │    70   │
│   55 mm   │  112.3  │    90   │
└───────────┴─────────┴─────────┘

And here is a drawing, to scale:

zoom at 18, 35 and 55 mm

The sensor is at the right. The intermediate image (not drawn) is 35 mm to the left of the front element. The interesting thing is that the movements of the groups (both front and rear) match what I've seen on most small mid-range zooms. A real zoom may have more groups (IS has been mentioned), but only two are really needed for the zoom action.

Example 2

For a more realistic example, see this patent for some Nikon 1 zooms. It's not the best example because these lenses are intended for a mirrorless camera. However, one of the embodiments is a 10-30 mm midrange zoom (27-81 equiv.), quite close in range to a 18-55 for 1.6×.

I like this example though because of the figures. Please take a look at the figure on page 1, and more specifically at the arrows at the bottom, below the labels “G1” and “G2”. These arrows show the way the groups move when the lens is zoomed from wide (W) to tele (T). You can see that the front group moves back and then forward, while the second group moves monotonously forward. That's what I have seen on many wide and midrange zooms, although not on all of them (not on the Nikkor 18-70 for example). You may notice that the second group has some subgroups among it, including one group for focusing (Gf) and one group for image stabilization (Gs). These subgroups are however irrelevant when one considers only the zooming action.

Anyway, the interesting thing here is that, although some of the provided examples have three lens groups, most (including the “preferred embodiment”) only have two. Quoting the patent (paragraph 077 on page 67):

An optical system according to the present embodiment includes, in order from an object side, a first lens group having negative refractive power, and a second lens group having positive refractive power.

This is exactly the description of a retrofocus lens.

Example 3

Here is another patent from Nikon which may be more relevant since it mostly describes the 18-55 kind of APS-C zooms.

Examples 1 and 2 of this patent are for such a simple retrofocus design, with a front group of focal length -31.51 mm and a rear group of focal length +37.95 mm. From the data tables we see that, as you zoom the lens from 18 to 55 mm, the front group moves first back (towards the sensor) and then forward (away from the sensor) while the rear group moves monotonously forward.

This patent shows also that the simple two-group design I am describing here is not the only possible option. Consider the example 5 of this patent. This lens has four groups that move all in different ways as the lens is zoomed. When zooming from 18 to 55 mm, the front group moves back, then forward, and the rear group moves monotonously forward. Thus, as seen from the outside, it looks like the simple two-group design of example 1, although internally it is quite more complex.

On the other hand, this particular design is actually not that far from the simple retrofocus design. If we say that groups 2, 3 and 4 constitute a sort of “super-group”, then the lens can be described as a group (G1) of negative refractive power followed by the super-group (G234) of positive refractive power. Still kind of a retrofocus. This description is not completely unreasonable as groups 2, 3 and 4 move more or less in the same fashion: they all move monotonously forward as the lens is zoomed from wide to tele, and their average movement is greater than the relative movements between them. From the table of lens data I calculated the focal length of this super-group and found that it does not change a lot: only from 38.6 mm at the wide end of the zoom to 34.8 mm at the tele end.

Although I have only investigated a few patents, my conclusion is that some sort of retrofocus design (but not necessarily with only two groups) is likely on a zoom if the following three conditions are met:

  • the lens is longer than its focal length at all settings
  • when zoomed from wide to tele, the front element moves first back (closer to the sensor), and then forward
  • when zoomed from wide to tele, the rear element moves always forward.

The first condition is likely to be always met by SLR zooms having a maximum focal length of no more than 55 mm.

PS: This answer has been heavily edited in order to better merge several edits. In the process I incorporated an important point raised by Stan Rogers, namely that the simple design is not the only possible design.

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Can you explain in very simple language why this makes a typical 18-55 lens start at middle length, then decrease, and then increase? –  mattdm Dec 26 '11 at 23:17
    
Because, with a converging group, the distance between the object and the image is minimum when the magnification is -1. Thus, starting at low magnification, as the magnification increases the distance first decreases and then increases again. –  Edgar Bonet Dec 27 '11 at 8:45
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And, while I hate to ask you I prove a negative, since the accepted answer and wikipedia article both include the idea that the function of the front group shifts from negative to positive, could you elaborate on that a bit more? It'd be particularly nice to show how this works with a typical 18-55mm. And, how would a lens with the tele/retro design behave w.r.t. lens extension? –  mattdm Dec 27 '11 at 14:38
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@mattdm: a magnification of -1 means that the image has the same size as the object, but is reversed. In macrophotography one would instead say “1:1”, forgetting the sign. And it's not “-1 something”, as magnifications have no units. By “zooming in (resp. out)” I mean turning the zoom ring towards longer (resp. shorter) focal lengths. –  Edgar Bonet Dec 27 '11 at 21:45
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@DragonLord: If you define a telephoto that way, then you have to measure the length of the lens from the front element to the image plane. In this example the length defined this way is 112.3 mm. –  Edgar Bonet Dec 29 '11 at 11:49

See edit note below this answer.


The lens is retrofocal at the wide end and telephoto at the long end. A retrofocus lens is referred to as "inverted telephoto" because it is constructed similarly to a telephoto lens with the elements reversed. The effect decreases as you zoom in, until you reach about 35mm, at which the lens begins to extend and eventually becomes a telephoto configuration, where the size of the lens, front element to rear element, is less than the focal length. The lens is neither retrofocal nor telephoto between these positions. This results in the lens being longer at the extremes of the zoom range than at intermediate positions.

For more information on this design, see the Wikipedia articles on Angénieux retrofocus, which discusses the origin of the design for the wide end, and telephoto lens for what happens at the long end. According to the telephoto lens article:

Zoom lenses that are telephotos at one extreme of the zoom range and retrofocus at the other are now common.

This is essentially what is happening with your 18-55mm lens. As far as I am aware, Canon, Nikon, Pentax, and Sony (A-mount, not E-mount) 18-55mm lenses all share this design aspect.


Edit: This answer is incorrect because it is based on an incorrect definition of "telephoto lens". Please disregard this answer; Edgar Bonet's answer is likely to be correct. See http://meta.stackexchange.com/a/22633/160017.

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These lenses are often telephoto at the other end as well (as opposed to merely being long), and will be neither retrofocus nor telephoto at some point in the tranformation (that is, the optical center of the lens will be at the actual focal length). So, at the shortest focal length, the front group is divergent and the rear convergent, at the longest the front is convergent and the rear divergent, and in the middle the whole thing acts as a single, complex convergent lens. That's a lot of parts shifting around. –  user2719 Dec 26 '11 at 9:09
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@EdgarBonet, this may be true for prime lenses, but the lens in question is a zoom lens. As such, the lens configuration can change from retrofocus to telephoto as you zoom from wide to long. –  DragonLord Dec 26 '11 at 14:50
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Mmm... interesting. Do you have an example of a design that achieves that? –  Edgar Bonet Dec 26 '11 at 15:00
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@EdgarBonet It's actually more than four independent groups in real life (especially if image stabilisation is involved) and no, it's not "overly complex". The transition from telephoto to retrofocal configuration can be explained by the relative movement of a single group in the simplest possible design -- the shifting of a convergent group between front and rear divergent groups, making the front and rear "group of groups" relatively more or less convergent/divergent. It's really a pretty elegant concept. –  user2719 Dec 27 '11 at 14:57
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The "simplest possible design" is not optically the best design. Rather than moving a central "supergroup" in relation to two fixed divergent elements/groups, it's the divergent elements that move in relation to the convergent supergroup. When the front divergent element is farthest from the center, you are at the shortest focal length. Conversely, when the rear divergent element is farthest away, you are at the longest. When the lens is at its most compact, it acts as a simple multi-group lens (neither retro nor tele). The central supergroup itself may be varifocal. –  user2719 Dec 27 '11 at 15:34

With most zoom lens designs as you zoom in, the lens barrel and front element will extend, that is true.

But there are some lenses like the Canon EF 24-70 where the lens is fully extended at 24mm and fully retracted at 70mm. So judging by the front elements, it seems to be working backwards!

And there are IF (internal focus) zooms where the front element doesn't move at all.

Any lens will have many groups of elements, some of which will be moving "out" and others moving "in". I guess the simple answer is you can't just judge by what you see the barrel and front element doing, there is a lot more going on inside. Some lens designs are very complicated. I'll be very interested if someone can post a simple picture to explain how this particular lens design works.

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