Constant Aperture Zooms, Geometry?

I read a post on photo.net dealing with TCs and depth of field. The

basic reasoning was that with a 1.4x for example a 200mm 2.8

effectively becomes a 280mm 4.0. The ratio between the new focal

length and the existing aperture changes the geometry to a 4.0.

Therefore the depth of field is like a 280mm lens with 4.0 aperture

not 2.8. Makes total sense. But then I began to think about

constant aperture zooms like 70-200mm 2.8. I'm stumped. How can

this be geometrically possible?

First of all, don't take the aperture thing too literally. The aperture is the size of the entrance pupil, which is a somewhat abstract quantity and may not correspond to any physical quantity. In particular, it's related to, but generally not the same as, the diameter of the diaphragm. It does correspond exactly to the _apparent_ diameter of the diaphragm as viewed through the front of the lens.

 

A constant-aperture zoom keeps its aperture constant by varying the entrace pupil diameter along with the focal length. In the classic design, the diaphragm remains the same physical size, but it moves in relation to the front groups of the lens. So if through the lens from the front as you zoom it out, the diaphragm opening will appear to be getting larger, even though in most designs it isn't. It's just the magnifying effect of the front groups. But again, it's the apparent diameter that matters, as this is the same as the entrance pupil.

 

Without an optics course, that's about as well as I can explain it.

So Mark, in other words what you are saying is that the minimum aperture is a factor of both the physical size of the diaphram as well as the diameter and magnification of the front elements? Would'nt the diaphram have to travel to the rear to have greater magnification from the front.

You may wish to read Photo.net's <a href="http://www.photo.net/learn/optics/lensTutorial">lens lutorial</a>, and perhaps its <a href="http://www.photo.net/learn/optics/lensFAQ">lens FAQ</a> as well.<p>To answer your questions, Jorge, Mark didn't say the diaphragm travels forward when you zoom to a longer focal length. "Zooming out" has become somewhat idiomatic for 'setting a longer focal length' as most zoom lenses get physically longer when you do that. All you need to do to render the aperture larger from the front, is to move an optical group with a positive focal length away from the diaphragm. The lens' physical length can remain the same while you do so. Let's keep in mind that varying the focal length of a lens implies much more than just moving one group! Virtually any group moves relative to all others in modern zooms.<p>The front element's diameter doesn't matter directly in this while its "magnification" does: if you replaced a lens' front group with one of equal optical parameters (surface curvatures, focal lengths, refractive indices, Abbé numbers, etc.) but of different diameter you'd get a smaller entrance pupuil if you used a group with a smaller diameter--because the original group is designed to be just large enough to avoid that, in order to keep elements' sizes and hence manufacturing costs in check. But with a group of a larger diameter, nothing would happen to the aperture--its maximum size would still the same.

"Mark didn't say the diaphragm travels forward when you zoom to a longer focal length"

 

Yea, I realized that after I answered his reply. But, wouldn't the diameter of the front elements come into play as well. You can magnify to a point and then it would stop at the edges of the front element. In other words you would have to increase the diameter of the front element relative to the focal length to increase the apparent aperture given a diaphragm of the same size. The logical (seems to me) approach would be to do a little of both increase the size of the diaphragm some as well as the diameter of the front element.

"In other words you would have to increase the diameter of the front element relative to the focal length to increase the apparent aperture given a diaphragm of the same size. "

 

Not if the front element is already big enough at the long end of the zoom. For example, the 70-200/2.8 has a front element large enough to generate f2.8 at 200mm. At 100mm it only requires about half that diameter to generate f2.8, depending on the location of the optical center and aperture of the lens. (f-stop = lens focal length divided by *aperture* diameter) Thus in theory, a 70-200/2.8 zoom could quite probably be designed as a 70-200 f2-f2.8 zoom without a significant size change.

 

Cheers,

As Jack explained! I know it's difficult to understand; whenever I encounter such a problem, I try to visualise things:<p>Look at a few lens diagrams, e.g. via the <a href="http://www.canon.com/camera-museum/camera/lens/f_lens.html">lens hall</a> of the Canon Camera Museum. (Click on a lens and then on "block diagram".) You'll see that all tele zooms have front groups whose focal lengths are positive--i.e. you could use these groups as loupes. Where do we find real loupes? Closeup lenses are nothing else. Let's take Canon's 500D: it comes in various filter thread sizes from 52 through 77mm. The magnification they provide is exactly the same, though the lens' diameters vary with thread size.<p>Someone will ask why no manufacturer offers a 70-200mm/<i>f:2.0-2.8</i>. As Jack wrote, in would be easy to design "<u>in theory</u>"; in practice, a number of optical flaws, especially spherical and chromatic aberration, would cause such a lens either to render bad image quality, or to be extremely expensive. Correction of these aberrations is why the the front groups of virtually all current lenses contain more than one element.