Marc Sabatella (marc@outsideshore.com) wrote in rec.photo.digital.slr-systems:

Although this is the way it works for probably 99% of zoom lenses, I have
a Sigma 24-70/f2.8 that is shortest at 60mm.  It lengthens very slightly
(less than 5mm) as you move to 70mm, and lengthens a *lot* (about 40mm)
when you move to 24mm.

Yeah, it's weird, but it's a good lens, and in the Minolta AF world,
there's really nothing else in that range that comes close in quality.
   

According to My Names Nobody <nobody@msn.com>:

    *Whose* naked eye?  The actual size of the image on the retina
is a function of the size of the individual eye.  You are not seeing a
*size* at a distance, but an *angle*.

    Quite simple -- the instruments which you make (other than the
video camera) are designed to go in front of human optical equipment
(eyes), and they *increase* the size of the image by a specific factor
on *anybody's* retina.

    And the video cameras are not giving you zoom related to a
"normal" view, but rather a ratio between the widest and the narrowest
angles of view.

    35mm camera lenses, are designed to produce an image on a
sensor.  Originally film, and those lenses are now being used to form
images on the digital sensors of cameras made to accept the same lens
mount.

    Note that you can't simply hold a telephoto lens in front of
your eye and see a larger image.  It has to be formed on something, even
a virtual image (in air) with a secondary lens to reformat it for
feeding into the individual's eye.  And if you use the secondary lens,
the magnification which you see looking though the combination of the
secondary lens and your camera's lens is going to be a function of both
the focal length of the camera's lens and the magnification of the
eyepiece.  (This is equivalent to changing the size of the sensor in the
camera.

    And photographers who have come to this from the 35mm world have
a natural feel for what a given focal length lens will give them, and
only have to adjust their expectations for the size of the crop factor
for their particular camera.

    Now -- there are optical devices for 35mm and DSLR cameras which
*are* rated with a magnification factor.  Those are telextenders, which
go between the body and the lens which you normally use, and they
increase the size of the image from a given lens by such a factor.  (I
think that the most common factors are 1.5X and 2.0X.) In the process,
they also reduce the effective maximum aperture of the lens -- you get
less light in exchange for greater image size.

    1/32 of an inch on *what*?  As I mentioned above, the size of
the image on the retina of the eye depends on the physical dimensions of
the individual's eye.  The one inch bumble bee at 30 feet is not a
*size*, it is an angle.  In particular, nine minutes, 32 seconds, or
0.1592 degrees in decimal.  The size of the image produced from that
angle is a function of the focal length of the lens, but "no
magnification" is meaningless here.  In my previous followup elsewhere
in this thread, I explained how you need to pick a standard 50mm for a
35mm film camera) which is close to producing the same angle of view (on
a print of a given size, viewed at a specific distance).  It is this
which defines a "normal" lens for a given sensor.  And everything else
needs to be compared to that.

    Again -- a function of what you call a "normal" for that
camera/sensor.

    A 50mm focal length lens is considered by most to be "normal" on
a 35mm film camera body.  There are others who prefer something
somewhere in the range between 42mm and 50mm.

    A normal lens on other cameras is a function of the size of the
film.  IIRC, a "normal" lens on a 2-1/4" square camera (TLR or something
like a Hasselblad) is 80mm.  The lens which came with my 4x5" Crown
Graphic is 135mm -- certainly within the "telephoto" range for 35mm
film.

    Actually -- it is closer to an 8X magnification -- when compared
to a 50mm lens.

    It seems to me that the normal users of SLRs have found that the
existing information -- the actual focal length range of the zoom -- is
much more usable information.

    And remember that the built-in zoom lenses in digital cameras
are rated not in magnification relative to "normal", but rather
magnification change from widest to narrowest field of view.

    You *must* include equipment specifics to get the kind of number
which you are looking for.  Anything else is meaningless.

    Enjoy,
        DoN.

It's not impossible, it's just not a useful metric, so no one does it.

Yes, it can, but for YOU to figure out the optical magnification given
a lens and camera spec, you need to define 1x magnification in terms of
something you know.  So you start with the "normal" lens focal length
for the format, which is 1x magnification, and then you can figure out
the magnification factor provided by a given focal length.

Camera lenses are *never* specified with that kind of magnification factor,
so no, you can't do that kind of comparison.  When a P&S camera is said to
have a "10x zoom", that does *not* mean 10x magnification; it means that
the longest focal length is 10x the shortest focal length.

If you do the above procedure to figure out the optical magnification, the
resulting number is not useful for comparison with any camera's zoom specs.

Because you look through a telescope, but you print out a photo. When I
look through a pair of binoculars, I am enlarging the image on my
retina, to be (say) 10x the size of the original. "Huh," I say, "these
binoculars have 10x magnification."

But when I take a picture, I can print it at wallet size, or 4x6, or
8x10, or 20x30. I can look at it from six inches away or from the other
side of the room. Every time I do that, the image changes size on my
retina, occupying more (or less) of my field of view.

Now, this doesn't mean you can't define a 1x magnification. I could
(watch me!) arbitrarily say that "A 1x lens will allow me to take a
photo of a tree, print it out at 8"x10", hold it in landscape
orientation at arm's length, and have the resulting image look exactly
the same size as it did when I was standing there."

No problem; we can do that. Assuming your arm is one metre long, that
10" wide photo is going to take up about 10 degrees of your field of
view ( atan(17.5 cm / 100 cm) = 9.93 degrees ). So, if the camera lens
had a 10 degree field of view, I should be able to print out the
picture, hold it in front of me, and have it blend seamlessly into the
surroundings. Tada, it's 1x magnification! As it turns out, a 200mm
lens on a 35mm camera has about a 10-degree field of view, so without
further ado:

A 200mm lens on a 35mm camera is a 1x lens
A 50mm lens on a 35mm camera is a 0.25x lens
A 200mm lens on a 35mm camera is a 1.5x lens
A 18mm lens on a APS-C camera is a 0.14x lens
A 6mm lens on a Canon S3 IS is a 0.18x lens

As it turns out, these are pretty silly numbers; more less than 1x than
greater. So apparantly I picked bad assumptions; maybe assuming an
11x14 print at half a meter would have given me numbers more in line
with what we're looking for.

But that's the problem right there. The size of the print, and the
distance at which the print is viewed, changes the apparant
magnification of the image. A telescope doesn't have this problem: You
look through it, and your eye is always in the same place with respect
to the lens. Nothing changes size, nothing changes distance.

That doesn't mean it's not possible; I've just proven that it is. But
it's arbitrary. Change the assumptions you make about print size and
viewing distance, and you change the magnification numbers you get. And
when you examine the process, you realize that all those assumptions
did is tell me that a 200mm lens on a 35mm camera is 1x, and all the
other calculations were made off of that. This is exactly what I
originally suggested: You need to pick a baseline for comparison. My
original choice of a 50mm lens on a 35mm camera was based on a common
photographic tradition; my new choice is based on some calculations
made from arbitrary assumptions.

So instead, we measure lens magnification based on the lens's focal
length. This is an inherent property of the lens. A 35mm photographer
will know that a 100mm lens makes things big and a 28mm lens makes
things small. As odd-sized digital sensors got common, the idea of a
"35mm equivalent" focal length gained popularity, exactly so that
people had a good non-ambiguous way of understanding the optical
effects of their lenses when combined with their cameras.

Not really; if nothing else, the camera is important. I have a 50mm
lens that I use on my Digital Rebel. If I took a picture with it, and
then gave the lens to my sister, she could take a picture with it with
her 35mm film camera from the same location, and when we printed the
pictures, hers would look more "zoomed out" than mine. Canon can't
stamp a big "1x" on the side of the lens, because it's going to behave
differently depending on the camera you put behind it. But they can
engrave "50mm" on the lens; that never changes, and it's up to the
photographer to understand what that means when it's combined with his
or her camera.

Looking at it another way: 35mm equivalent focal lengths -are-
equipment non-specific. Every lens/body combination has a 35mm
equivalent focal length, which describes exactly how much "zoom" you
will get. Why 35mm? Why not? Most photographers are familiar with it,
and those that aren't can learn it or convert it to some system they
know better (like APS-C equivalent, or
angle-of-view-when-printed-at-8-x-10-and-held-a-meter-away equivalent).

This goes back to the bulk of my response, up above: 1/2 an inch on
what size print? On the film negative (or digital sensor) itself? The
frame is rather small, and is almost always enlarged to at least some
degree before you actually look at it.

It's only the common baseline among people that use 35mm cameras,
compact digital cameras, and DSLRs. Talk to a medium- or large-format
photographer (I am neither) and I'd be very surprised if they use 35mm
equivalents when discussing their lenses.

I just did, results are above, free for the world to use :-) I think
they suck, though. Really, 200mm as a 1x lens? That's just silly.
Improvement on this is left as an exercise for the reader...

I've only seen this in one photographic context: Macro lenses. They're
commonly quoted as being 0.5x (low-end ones), 1x (most decent ones),
and I've seen as high as 5x. This is comparing the size of the object
in real life to the size of the image on the film/sensor. This means,
though, that when a print is made from a picture taken with a 1x macro
lens, the image on the print will be larger than the object actually is
in reality. The 1x is very counterintuitive here. They're also
described as ratios (e.g. 1:2, 1:1, 5:1), possibly to try to avoid
exactly this confusion.

- Darryl

That might be the baseline *you'd* like to use for comparison, but it is
*not* the baseline actually used when you see cameras with zoom lenses
quote magnification ratios. A point & shoot camera that advertises a
"7X" zoom is not saying that it magifies things seven times more than
"what the naked eye sees", but rather, that its maximum magnification is
seven times its minimum magnification.  Most likely, the minimum
magnification is a little more than half "what the naked eye sees" (to
the extent it makes sense to define this at all - see below), and the
maximum magnification three to four times "what the naked eye sees".
Whereas another zoom lens might be only "4X", but that might mean
minimum is twice "what the naked eye sees" and the maximum is eight
times "what the naked eye sees".  Meaning the 4X zoom would actually
magnify more than the 7X.  That's why you don't see SLR lenses using
ratios like these.  You see real, hard numbers to give focal length.
The 7X zoom I mentioned would actually be sold as 28-200, the 4X as
100-400.  Then we could compare the focal length ranges directly to see
that the former did a lot more at the wide angle end of the range but
the latter did a lot more at the telephoto end.  This is all relevant
information, and that's why camera lenses are labelled with all of it.

Video camera zoom ratios are exactly like point & shoot zoom ratios.
That is, they aren't telling you how much a camera magifies comared to
what the naked eye sees, but simply telling how its maximum
magnification compares to its minimum magnification.  As for binoculars
and scopes, it is possible to come up with a definitive number for these
because the images are being projected on the same screen: your retina.
Now, if you want to take the lens off your camera and hold it up to your
eye like a telescope, you could similar come up with an absolute number
to measure the magnification.  But that number would only be meaningful
when projecting the image onto your retina.  It would cease to have
meaning when projecting the image onto a piece of film or a camera
sensor.  Because in order for that image to eventually get on to your
retina, it's going to have to be displayed or printed somehow, and you
have no way of knowing how much it is going to be magnified in the
process of displaying or printing it.

Not really, at least, not in the way you want.  See below.  The best
convention we have is that of a "normal" lens, which as has been
mentioned here, is considered around 50mm on a 35mm film camera, or
around 30-35mm on most digital SLR's.  What is relevant in making this
"normal" isn't so much magnification, since any picture can be blown up
bigger, but rather, angle of view - how much you can actually take in at
once without moving your eyes.  A normal lens is one that approximates
the angle of view that we typically see.  Of course, that differs
between people, and since our vision isn't constant across our field of
view but rather drops off toward the edges (and at different rates for
things close up than things far away, most likely), there is some leeway
in defining even for a given person what his angle of view is.  But
there is general agreement that somewhere around 50mm is a "normal"
focal length for most people when projecting an image onto a piece of
35mm film.  And since most digital sensors are smaller than that, a
correspondingly smaller focal length is "normal".  Of course, it order
for that image to actually *look* normal, we'd have to project them onto
a wall that just barely fills out field of vision.  When looking at the
image printed 4x6, we sort of have an inutive sense of what looks
"normal" and what looks like it was taken with a longer or shorter focal
length length, but this can be deceiving.  It can be hard to tell the
difference between an object taken with a 50mm from 10 feet away versus
the same object taken with a 200mm from 40 feet away (actually, I'm not
sure I have the math right there - it might be 20 feet, or some other
number involving the square root of 2, to get the object to appear the
same size on a same sized print, but whatever).  Still, the notion of a
"normal" lens is the closest you're going to get to "what the naked eye
sees".

So if you want to compute a "magification" factor in this way, divide
the focal length by, say, 33 for most digital SLR's or 50 for a 35mm
film SLR or "full frame" digital.  Thus, the aforementioned 28-200 zoom
would not be called a "7X" zoom, but rather, a ".6X - 4X" zoom on a 35mm
camera, or a ".8X - 6X" on most digital SLR's.  That is, you'd list the
magnifications at both ends of the zoom range, not just the ratio
between those magnifications.  And indeed, one *could* do this.  But I'm
not sure I have any intuitve sense of what ".6X" or "4X" looks like.
The only way to know would be get a feel for it through experience.  And
one can develop a feel for what "200mm" looks like just as surely as one
can what "4X" looks like.  So I don't see what is gined by this
approach.

1/32 of an inch where?  On your retina?  If you hold out a ruler at
arm's length?  This is problem #1 with computing what sort of
magnification we are talking about in absolute terms.

1/2 an inch where?  On the camera sensor?  When you display it on your
comuter screen?  When you make a 4x6 print?  When you project it on a
wall?  That's problem #2 with computing what sort of magification we are
talking about in absolute terms.

No, because such a thing is quite impossible to do for the reasons
described.  Howeve,r it is trivially simple to divde focal length by 50
or 33 to get something resembling what you are talking about if calling
a 200mm lens a "4X" zoom has more meaning to you than simply calling it
a 200mm lens.

---------------
Marc Sabatella
marc@outsideshore.com

Music, art,  & educational materials
Featuring "A Jazz Improvisation Primer"
http://www.outsideshore.com/

Well, to have any type of coherent discussion, it's pretty important to
agree on the basic terms.

Magnification is a ratio. 1:1 magnification is no magnification; the
final image is the same size as the starting image. 2:1 magnification
makes the final image twice as big as the initial image, etc. Those
ratios are equivalent to magnification factors of 1.0 and 2.0; a
magnification of 1.0, or 1:1, or 1x, or however you write it, is indeed
"no magnification".

The problem with writing "zero magnification" is that, while it's
perfectly valid on its own (i.e. it's synonymous with "no
magnification"), the usage of a number opens the door to potential
confusion. The phrase "0.5 magnification" is commonly understood to
mean "half the size"...this raises the question of what "0
magnification" should be.

The phrase "zero magnification" has a perfectly valid meaning according
to the strict dictionary definition, but in this context something like
"1x magnification" or "no magnification" is less likely to cause
confusion.

- Darryl