Posted by Larry Fischer on December 8, 2009 at 5:03 PM
Following the question on lens diameter I would say I understand the ratio of lens diameter to lens focal length at maximum aperature as being the f-number.
I also understand that for most SLR that 50 mm means about 1:1 ratio on the film plane.
Why then don't we describe lenses based on the photo plane ratio magnification? Isn't that what 14mm, 28mm, 50mm, 300 mm really means?
A 28 mm f/2.8 allow less light than a 28 mm f/2.0 at full aperature.
But don't the both have the same optical field width and height?
I don't care to much about the lens being described as 28 mm.
I like the description of a 71-degree f/2.8; or, 5-degree f/2.8, etc., or some description of magnification like 1/2:1 f2.8 for 28 mm or 6:1 f/2.8 for 300 mm.
We have to do the conversions for FX and DX differences anyway and those figures could, upon use, be more meaningful.
the fisch
Posted by Basil Greber on December 8, 2009 at 5:22 PM
Holy cow, now you got me terribly confused... sorry.
Posted by David Bostedo on December 8, 2009 at 5:34 PM
Larry - I personally never think about lenses in terms of magnification (and I'd guess many shooters don't care what it is - I know I don't), so for me focal length or field of view make more sense. Focal length and field of view (FOV) are equally valid I guess, but focal length is a little more obvious to me since it seems to relate to a physical attribute of the lens, as opposed to the result of that physical attribute.
As far as magnification goes, it doesn't really work since it doesn't uniquely describe a lens. To say that a lens can do a magnification of 1:1 doesn't tell you much about the lens. The magnification varies depending on sibject distance, focus point, and lens distance from sensor/film, whereas focal length or FOV are always fixed for a given lens.
Posted by Buck Ward on December 8, 2009 at 6:19 PM
A 1:1 ratio is an indicator of a macro lens. It's sometimes called the reproduction ratio. A 50mm lens is usually referred to as a normal lens or standard lens. On a 35mm film camera or a full frame DSLR, the field of view supposedly is similar to what we see with our eye. But it won't give you a 1:1 ratio on the film plane, unless that is, it's a 50mm macro lens. My old 50mm Micro Nikkor only came me 1:2. An extension tube was needed to achieve 1:1.
The f-number is based on the ration of the diameter of the aperture to the focal length. Lenses of different focal lengths but with the same f-number will give you the same exposure. If you need an aperture of f2.8 at a given shutter speed, the focal length is irrelevant.
All other things being equal, a 50mm lens will give twice the magnification of a 25mm lens, and half the magnification of a 100mm lens. But - if the lens won't focus close enough to your object, you're not going to get a reproduction ratio of 1:1 (i.e. life size) at the film plane. If you could get a 1:1 ratio with a 100mm lens, then you could get the same ratio of the same subject at twice the distance with a 200mm lens. For the reproduction ratio, the f-number is irrelevant.
The series of f-numbers, 2, 2.8, 4, 5.6..... are multiples of the square root of 2, or approximately 1.4. When you increase the diameter of the aperture by a factor of 1.4, you double the amount of light that can reach the sensor. When you double the diameter, the amount of light passing through quadruples. The reproduction ratio remains the same.
I think the field of view (FOV) for different lenses of the same focal length should be the same, regardless of the maximum aperture of the lenses, e.g.. f2 vs f2.8, though there may be some variations due to optical design.
Lenses are commonly referred to by their focal lengths. It's what we're all used to, and I can't imagine that it's going to change. It's amusing to me that in the US, an English system hold-out, focal lengths are expressed in metric terms these days. Ansel Adams referred to the focal length of his lenses in inches. Throws me for a loop when he says he used a 10-inch lens.
Posted by Larry Fischer on December 8, 2009 at 6:21 PM
Thanks guys.
David B., would not magnification tell you as much as focal length?
We are used to focal length but there has to be a touchstone focal length by which all others are measured. Therefore, doesn't 1:1, no magnification (perhaps at infinity) become a 50mm lens for FX??
If, and I say if, that is true, then would not a 2:1 lens be 100 mm? I do that all the time in reverse to see about what power by which I'm magnifying. When I hoist my old 500 mm Nikkor reflex I figure I'm looking through 10 power magnification on my FX digital. Why not just put that on the lens? And it now must be equated to sensor size whereas before 35 mm film was standard. (Perhaps with the different sensor sizes focal length might be better than using magnification???)
I guess I'm trying to equate focal length to magnification and how we got started using focal distance rather than magnification (perhaps always at infinity)??
You all might have better things to do. I'm partially snow bound right now.
the fisch
Posted by Richard Ditch on December 8, 2009 at 7:02 PM
Focal Length is the distance from the nodal point of the lens at which light from infinity is brought to a point of focus. Look at any simple ray diagram of a lens with parallel lines of light from infinity passing through the lens and coming to a single point one focal length away. That's a pretty specific and easy to understand parameter for any lens. Move that lens 2 focal lengths away from the focal plane and you get a 1:1 magnification ratio governed by the basic equation of optics:
This equation works with ID = OD = 2*FL to give 1:1.
The relationship of the so-called "normal" 50mm lens for a 35mm camera is that the diagonal of the 24mm x 36mm film chip is about 43mm and you get an angle of view similar to normal human vision when the focal length of the lens matches the diagonal of the film.
The reason we write f/# for the aperture is to indicate the ratio of the diameter of the opening to the focal length ("f" represents Focal length, "/" represents "divide by"). So an f/2 lens has a maximum aperture diameter of (focal length)/2 or half the focal length.
Why then don't we describe lenses based on the photo plane ratio magnification? Isn't that what 14mm, 28mm, 50mm, 300 mm really means?
Because "photo plane ratio magnification" doesn't mean anything as far as I can tell. And because 14mm. 28mm, 50mm, 300mm actually mean something: the distance from the nodal point to the film plane for infinity focus.
I don't care to much about the lens being described as 28 mm.
Well I certainly do. It tells me how far away from the film plane the lens has to be for infinity focus. It tells me how much extension I need to add to get a certain reproduction ratio. And from 60+ years of 35mm format history and literature and experience it tells me what to expect when I mount it on my camera body.
Posted by David Bostedo on December 8, 2009 at 7:28 PM
We are used to focal length but there has to be a touchstone focal length by which all others are measured. Therefore, doesn't 1:1, no magnification (perhaps at infinity) become a 50mm lens for FX??
Short answer? No. As others mentioned above, there are dependencies for magnification. Maybe there's some confusion over what "magnification" means? It's the ratio of the physical object size to the size of the object in the imaging plane (at the physical sensor or film). It doesn't depend at all on the format of the camera. So the magnification of a lens at a particular subject distance and focus distance will be the same regardless of whether you have an FX camera or DX camera.
For instance, if a lens is 1:1 at a certain subject/focus distance, and you're photographing a 1 cm long subject, it will create a 1 cm long image inside the camera. It doesn't matter what size the sensor is. The reason you might need a macro lens is that a lot of lenses won't let you get close enough and focus close enough to actually acheive this. That's why a 50mm macro and a 50mm standard lens won't be able to do the same magnification. And THAT'S what I meant by magnification not really describing the lens directly. It's a secondary property and doesn't necessarily tell you much.
That's also why others above pointed out what you might be thinking of - that a 50 mm lens approximates the human FOV on 35mm film or an FX sensor. That doesn't at all mean the magnification is 1:1.
I'm also not sure what you mean by "touchstone focal length" or "by which all others are measured". Focal length isn't a ratio or a comparison value - the focal length is literally a physical property of the lens. It translates directly to a FOV, but not necessarily to a maximum magnification, because that's dependent on some other factors. And that's why I typically ignore magnification - I don't usually care what physical size an object shows up as on my sensor, I just care how much of the frame it fills for the composition I want.
Posted by Dan Borzynski on December 9, 2009 at 12:52 AM
The other issue is that your definitions are also format dependent.
In 4x5, 150mm is approximately the same as a 50 mm lens in 35 mm based gear (digital or film). So under your system, is this a 3:1 lens or a 1:1 lens? You can rig up a LF back to use your 35 mm based body. If you start with a 150 LF lens, is it still a 3:1 lens? 1:1? 1:3?
But 4x5 has different proportions than 35, so is a 135 mm or a 165 mm a better normal lens equivalent? I've seen both argued.
And how about something really odd, like 6x24?
As it currently stands, everyone knows what a 28mm lens looks like through the viewfinder, 50 mm, 100 mm, etc. Also, most photographers, once they have gone through a discussion on magnification, understand that 1:2 is half life size on the recording medium and 2:1 is twice life sized. This is a universal through the camera world. Changing that, especially being so far removed from the origins of the system (from equipment that predates 35 mm by a century or so) doesn't solve any problems that currently exist.
Posted by Jim DeWitt on December 9, 2009 at 1:28 AM
In addition to the other points, the sensor size is another complicating factor. I use the Olympus 4/3 system. The smaller sensor adds a further level of complication if you use something other than the lens length as described by Richard you seriously confuse the issue.
Posted by Jim Bullard on December 9, 2009 at 8:02 AM
Any lens at twice its focal length from the film/sensor is a 1:1 lens whether it is a 150mm at 300mm from the image plane or a 28mm at 56mm from the image plane. The optical length of a lens is the distance to the optical center (not necessarily the physical center) to the image plane when focused on infinity. To focus nearer you must move the lens farther from the image plane. At twice the rated focal length you hit the 1:1 ratio. farther than that the image becomes larger than life size. Given a long enough extension tube or bellows any lens can be 1:1.
There are all sorts of things that complicate that optical principle which is based on a 'simple' lens. Things like modern lens design which uses multiple lens elements to bend the light rays in different ways creating lenses which are physically shorter than their optical characteristics would indicate. An easy example of that is the + diopter or "close up" lens which, like a pair of reading glasses, allows the lens to focus closer without moving the lens farther out. Like wise zoom lenses use moving internal elements to alter the angle of view.
Without a focal length we would not have the f/stop which is nothing more than a fraction. f/16 for example has a diaphragm diameter of 1/16th the focal length of the lens. Because the diameter is derived from the focal length of the lens f/16 on a 100mm lens is a larger opening than f/16 on a 50mm lens which in turn is larger than the opening on an 18mm lens but... the amount of light reaching the image plane at any given f/stop is equal for all focal lengths. That is due to the law of inverse squares which is a whole 'nuther discussion and I can see everyone's eye's glazing over already.
Yeah, I'm a techie. OTOH being a technical photographer means I understand what's going on under the hood and that is helpful to understanding how we got to where we are.
Posted by Larry Fischer on December 9, 2009 at 8:26 AM
Good answers all. But I have more.
Is the nodal focal point to film plan a measure of "wideness"??
From memory I think my Nikkor 28 mm is about 71 degrees in width. Other lenses have a "width" also but I don't know the specs. Is there a relationship between focal plane distance and width?
If so, would not that also be a form of magnification?
I've done some astrophotography and telescopes are rated by 1) aperature, which is the lens diameter for light gathering, and 2) focal plane distance. The higher the number the greater the magnification. There is no diaphragm to change the f/number. I guess that function might fall to the occular lens???
A telescope is just a fixed aperature lens and the occular is basically rated in millimeters for additonal magnification of a portion of the image.
Now, a camera attached to a telescope records the image at the focal plane distance. When extension tubes or Barlow lenses (2x) are attached, the focal plane distance is increased and so is magnification. There has to be a mathematical relation to this.
And in microsopes we speak of magnification (diameters), not millimiters. My microscope has 4 objectives and a 10 power occulars (binoc). So I get from 3.5, 10, 40 and 100 x objectives a total magnification of 35x, 100x, 400x, and 1000x. To me this just makes more sense than speaking in terms of 'lens nodal point to film/sensor plane'.
I understand that tradition allows us to be comfortable with how we use these numbers. I'm just asking if my statements are true, which most info coming in says no, but if they were/are, then I would like a magnificaton number. I'm always comparing to binoculars.
And thanks for the time you've spent. I'm archiving some of the replies.
the fisch
Posted by David Bostedo on December 9, 2009 at 8:57 AM
Larry - I don't know too much about telescopes, but I do know this : the definition of magnification for a telescope is different, IS related to FOV (and therefore focal length) directly, and makes more sense in that world. Maybe that's why there's some confusion.
The reason it's directly related to FOV is that it's defined by the percent of the FOV that something appears to cover. So if the moon is 2 degrees of view in the sky with your eyes, and 30 degrees of the view in the eye piece, you have a 15X scope. But that works because the earth is essentially a fixed reference to what's in the sky. You can't switch your telescopes focal length, move it closer to the moon, and still acheive the same magnification like you can with cameras. That also means that magnification with telescopes is related to your viewing of it (the "medium") whereas the definition for a camera is medium independent. And cameras magnification varies with focus distance and camera-to-subject distance. I'd imagine this is so much less variation on a telescope it can be ignored.
There is no fixed reference with cameras. I can have a 100mm 1:1 magnification camera lens at 2m from the subject, or a 50mm 1:1 magnification lens at 1m from the subject. Just knowing that my lens is 1:1 wouldn't tell you as much as knowing that it's a 50mm or a 100mm, since that also determines the perspective/FOV.
There are some similarities, and you're right, if you play with the numbers there are relationship's between FOV, focal length, magnification - either camera or telescope definition - and probably a relationship between the two definitions. (Something like 15X telescope is the same as a 1:4 camera lens magnification - you just can't get close enough to the moon to actually get 1:4....something like that anyway, I haven't looked up any equations.) Maybe a good practical optics book would make for a good read. I don't have any suggestions there though.
Posted by Jim Bullard on December 9, 2009 at 4:56 PM
What we commonly call the nodal point is the point of the lens around which, if you rotate the camera, objects in its field of vision do not shift position in relation to one another. Strictly speaking that is not a nodal point but knowing where the point is useful in making stitched panoramas. It does have a relationship to angle of view in the sense that it varies in direct relation to the focal length which is what really determines the angle of view.
Addendum/correction: Field of view varies with the design of the lens too. Within any format the field of view varies in the manner I mention above however, a 300mm lens designed for 4x5 necessarily has a much broader field of view than a 300mm lens designed for 35mm film. In that sense it is a measure of a given lens which is not entirely dependent on its other characteristics.
Posted by David Bostedo on December 9, 2009 at 7:41 PM
One thing to mention with regard to what Jim said - the FOV varies depending on the format of the lens - not the format of the capture medium (film or sensor). Where this matters is in the digital world of different sized sensors with the same lens - the FOV the of the lens doesn't change no matter what the sensor is.
An example : pretend you have an FX ("full frame") camera, DX ("APS-C" or "1.5X") camera, and 300mm lens. If the lens image circle just barely covers the FX sensor, the FOV is about 8.25 degrees, and the image captured will be 8.25 degrees corner to corner. Switching to a DX camera, the same lens creates exactly the same FOV inside the camera - about 8.25 degrees. But what changes is the amount of that FOV captured - it's much smaller. So a DX camera would capture about 66% of the FOV, meaning about 5.5 degrees. This is what creates the focal length multiplier common to digital cameras. The same 300mm lens is :
300mm, 8.25 degree FOV on FX
300mm, apparent 450mm (often referred to as "35mm equivalent" or "mm-e"), apparent 5.5 degree FOV on DX
Thinking about this some more, there are cases where I'm not sure if actual focal length/FOV is used to name the lens, or an equivalent focal length is used to name the lens. Something like Canon's tilt-shift lenses create a much larger image circle than what's actually captured (to accommodate movements). So when we reference, for instance, the 24mm Canon TS-E lens, I wonder if the max image circle inside the camera is 24mm, or if 24mm is just what's captured on the sensor. If it's the latter (and I suspect it is) then that's actually 24mm-e, and the image circle is a wider FOV and shorter focal length.
Posted by Mark Stahlke on December 10, 2009 at 12:12 AM
Wow, this thread went some strange places. It looks like inconsistent use of terminology is causing some confusion. I think we have "magnification ratio" straightened out but there is some residual confusion about "angle of view" (or FOV, if you must).
Angle of view is related to the focal length and the film size. It works like this:
a = 2arctan(d/2f)
a is the angle of view f is the focal length d is the film dimension (horizontal, vertical, or diagonal)
Jim and David, I think you're conflating angle of view and angle of coverage. The angle of coverage is the angle of the cone of light coming out the back of the lens. The angle of coverage determines the size of the image circle. It's independent of the film size and focal length.
In David's 300mm lens example, the angle of coverage stays the same but the angle of view drops from 8.25 degrees to 5.5 degrees because the film size changed.
To help pull all this together I'll give another example. I have two lenses right in front of me. Both are spec'ed at 150mm focal length and f/5.6 maximum aperture. One has an angle of coverage of 72 degrees, the other is 105 degrees. The 105 degree lens has a huge image circle compared to the 72 degree lens. Both of these lenses will produce the same angle of view on 4x5 film - about 45 degrees on the horizontal (5 inch) side. And both lenses will cover 4x5 film with lots of room for movements.
On 8x10 film a 150mm lens will produce an angle of view of about 90 degrees on the 10 inch side. Notice that the required 90 degree angle of view exceeds the 72 degree angle of coverage of one of the lenses. That lens will not cover 8x10 because it isn't capable of projecting a 90 degree angle of view. Trying to use the 72 degree lens on 8x10 would result in severe mechanical vignetting - I would get a round image that didn't fill the entire sheet of film. The 105 degree lens covers 8x10 quite nicely, thank you very much.
So what about digital?
It's exactly the same. In terms of optical principles, digital sensors are just electronic film.
Getting back to Larry's original question, lenses are spec'ed by focal length because that's a physical property of the lens. Things like magnification ratio and angle of view will vary depending on how the lens is being used.
The really fun question, the question that keeps me up at night is: How do they make a zoom lens with a constant maximum aperture?
Think about it. I have a 28-70mm f/2.8 lens. At 28mm the maximum aperture is 10mm. At 70mm the maximum aperture is 25mm. How do they do that?
Pop! Fzzzzt!
Drat! there goes that fuse in my brain again.
Cheers,
Mark
Posted by Larry Fischer on December 10, 2009 at 8:16 AM
Mark, your explanation of angle of coverage being dependent of focal length makes sense. If I can write it in my own terms and it is correct, then I understand.
The angle of coverage is intially started by the lens. A lens with a large angle of coverage must have a short focal distance. If one could observe the light behind in the lens, say in a very dusty room, the angle formed by the light approaching the focal point would be the angle of coverage. The size of that spot is determined by where the film/sensor is placed within that cone of light.
The focal point of the lens does not change. It is a physical property of its glass and design. Yet in a compound lens the focus can change.
Now for the statements and questions:
Is the film/sensor plane at the focal point? Or is it manipulated by the focusing ring on lenses to maintain focus at the film plane? It would seem so but I keep thinking of my days as a child playing with a magnifying glass. The focal point of the sun directed through that glass would burn paper but it was a very small spot. The bigger the lens on the magnifying glass the hotter the focal point because more energy was passing through the lens. In terms of photography that would be a "faster" lens.
Now, again, is the focal point where the maximum energy in terms of light is placed on the camera or can film/sensor be in front of that focal point or focused in front for a larger circle of coverage? Is/can "focusing" the lens change any of this? I realize we are dealing with compound lenses and that probably adds major complications in my kid's toy.
Thanks for everyone's time. I'm learning-------I think (arc tangents !!!!!???? long time ago for me)
the fisch
Posted by David Bostedo on December 10, 2009 at 8:44 AM
Larry - The focal point will be somewhere internal to the lens. I just found this page on lenses which seems pretty good. Most lenses are pretty complicated internally, but this captures the gist.
angle of view will vary depending on how the lens is being used
That's the part that I didn't understand. I was originally assuming that a 300mm lens for 35mm will always have the same angle of coverage (I suppose you could call this the lens FOV, as opposed to the camera or sensor or image FOV) - until I realized that the tilt-shifts can't have the same angle of coverage.
So here's what I'm still wondering - and maybe someone can help. How is lens focal length specified for a lens? Is it the apparent focal length based on 35mm film? Or is it the true focal length which directly translates to angle of coverage, which is format independent?
I think it must be apparent focal length, since, as I mentioned above, a 24mm tilt-shift must have a larger angle of coverage than a 24mm standard lens. Therefore, 24mm is just the equivalent focal length based on 35mm film or a full frame sensor.
Right? And is that true of all lenses?
Posted by Jim Bullard on December 10, 2009 at 1:12 PM
Larry, The focal point is the distance necessary to have the subject matter in focus and varies with the subject distance. It is always the same in the magnifying glass experiment you mention because the sun is at infinity and never gets close enough to require moving the glass further from the paper (thank God. We'd all be toast if it did). Here's a link to a sharelesson that I wrote up many moons ago on the circle of confusion <http://www.northnet.org/jimbullard/CoC.htm>. It is from a dead website of mine that is still on an old server which now belongs to a different ISP than the one I used at the time and I can't get them to take it off but it should help understand the business of focus.
As I explained earlier the focal length is the distance from the the focal point to the optical center of the lens when focused on infinity. If your subject is closer you must move the lens further from the film/sensor plane. The focal point changes with the distance to the subject but the focal length of the lens does not. It is a fixed unit of measurement based on focus at infinity.
As you focus on things closer and closer the amount you have to move the lens away from the film/sensor increases in inverse squares. Focusing on something at 30 feet vs infinity requires a tiny movement whereas focusing on something at something at 3 inches vs 3 feet requires a much larger movement of the lens. Since light falls off in inverse squares as well this means that the physical opening of any particular f/stop results in less light falling on the film/sensor than the number indicates. Modern lenses for digital and 35mm compensate for that within the limits of design but those limits are why you will see zoom lenses rated f/3.5-4.5 or similar. The lens design does not allow the diaphragm to open enough to fully compensate when the lens is at its maximum extension so the actual value falls from 3.5 to 4.5.
Field of view is how broad an angle the lens sees (the angle in front of the lens). Field of coverage is how big the image circle is on the back side of the lens. Both vary with the design of the lens. A 65mm lens on a 35mm camera is nearly normal in its field of view but a 65mm lens for 4x5 is very wide angle. However if you put the 65mm lens designed for 35mm on a 4x5 camera its field of view (and coverage) would still be the same as it was on the 35mm and you would only get a small circular image in the center of the 4x5 film. There is an excellent demonstration of this by Ansel Adams on page 61 of BASIC TECHNIQUES OF PHOTOGRAPHY by John Schaefer. I highly recommend that book.
Posted by Larry Fischer on December 10, 2009 at 2:00 PM
Jim,
Good stuff. I'll visit your old website.
I think one item that I've not considered is the "focus" power of the lens compared to a magnifying glass.
I understand circles somewhat and the relation of "inverse squares".
Now, is the FOV the same regardless of focal distance, ie infinity or 3 feet.?
I would presume that at full aperature it would be the same because the angle of light falling onto the focal plane must be the same at a given aperature or with a specific lens. That feature, as was explained before, is inherent in the lens. It would give the same field of coverage.
Discussion
18 repliesI also understand that for most SLR that 50 mm means about 1:1 ratio on the film plane.
Why then don't we describe lenses based on the photo plane ratio magnification? Isn't that what 14mm, 28mm, 50mm, 300 mm really means?
A 28 mm f/2.8 allow less light than a 28 mm f/2.0 at full aperature.
But don't the both have the same optical field width and height?
I don't care to much about the lens being described as 28 mm.
I like the description of a 71-degree f/2.8; or, 5-degree f/2.8, etc., or some description of magnification like 1/2:1 f2.8 for 28 mm or 6:1 f/2.8 for 300 mm.
We have to do the conversions for FX and DX differences anyway and those figures could, upon use, be more meaningful.
the fisch
As far as magnification goes, it doesn't really work since it doesn't uniquely describe a lens. To say that a lens can do a magnification of 1:1 doesn't tell you much about the lens. The magnification varies depending on sibject distance, focus point, and lens distance from sensor/film, whereas focal length or FOV are always fixed for a given lens.
The f-number is based on the ration of the diameter of the aperture to the focal length. Lenses of different focal lengths but with the same f-number will give you the same exposure. If you need an aperture of f2.8 at a given shutter speed, the focal length is irrelevant.
All other things being equal, a 50mm lens will give twice the magnification of a 25mm lens, and half the magnification of a 100mm lens. But - if the lens won't focus close enough to your object, you're not going to get a reproduction ratio of 1:1 (i.e. life size) at the film plane. If you could get a 1:1 ratio with a 100mm lens, then you could get the same ratio of the same subject at twice the distance with a 200mm lens. For the reproduction ratio, the f-number is irrelevant.
The series of f-numbers, 2, 2.8, 4, 5.6..... are multiples of the square root of 2, or approximately 1.4. When you increase the diameter of the aperture by a factor of 1.4, you double the amount of light that can reach the sensor. When you double the diameter, the amount of light passing through quadruples. The reproduction ratio remains the same.
I think the field of view (FOV) for different lenses of the same focal length should be the same, regardless of the maximum aperture of the lenses, e.g.. f2 vs f2.8, though there may be some variations due to optical design.
Lenses are commonly referred to by their focal lengths. It's what we're all used to, and I can't imagine that it's going to change. It's amusing to me that in the US, an English system hold-out, focal lengths are expressed in metric terms these days. Ansel Adams referred to the focal length of his lenses in inches. Throws me for a loop when he says he used a 10-inch lens.
David B., would not magnification tell you as much as focal length?
We are used to focal length but there has to be a touchstone focal length by which all others are measured. Therefore, doesn't 1:1, no magnification (perhaps at infinity) become a 50mm lens for FX??
If, and I say if, that is true, then would not a 2:1 lens be 100 mm? I do that all the time in reverse to see about what power by which I'm magnifying. When I hoist my old 500 mm Nikkor reflex I figure I'm looking through 10 power magnification on my FX digital. Why not just put that on the lens? And it now must be equated to sensor size whereas before 35 mm film was standard. (Perhaps with the different sensor sizes focal length might be better than using magnification???)
I guess I'm trying to equate focal length to magnification and how we got started using focal distance rather than magnification (perhaps always at infinity)??
You all might have better things to do. I'm partially snow bound right now.
the fisch
1/(focal length) = 1/(image distance) + 1/(object distance)
This equation works with ID = OD = 2*FL to give 1:1.
The relationship of the so-called "normal" 50mm lens for a 35mm camera is that the diagonal of the 24mm x 36mm film chip is about 43mm and you get an angle of view similar to normal human vision when the focal length of the lens matches the diagonal of the film.
The reason we write f/# for the aperture is to indicate the ratio of the diameter of the opening to the focal length ("f" represents Focal length, "/" represents "divide by"). So an f/2 lens has a maximum aperture diameter of (focal length)/2 or half the focal length.
Because "photo plane ratio magnification" doesn't mean anything as far as I can tell. And because 14mm. 28mm, 50mm, 300mm actually mean something: the distance from the nodal point to the film plane for infinity focus.
Well I certainly do. It tells me how far away from the film plane the lens has to be for infinity focus. It tells me how much extension I need to add to get a certain reproduction ratio. And from 60+ years of 35mm format history and literature and experience it tells me what to expect when I mount it on my camera body.
Short answer? No. As others mentioned above, there are dependencies for magnification. Maybe there's some confusion over what "magnification" means? It's the ratio of the physical object size to the size of the object in the imaging plane (at the physical sensor or film). It doesn't depend at all on the format of the camera. So the magnification of a lens at a particular subject distance and focus distance will be the same regardless of whether you have an FX camera or DX camera.
For instance, if a lens is 1:1 at a certain subject/focus distance, and you're photographing a 1 cm long subject, it will create a 1 cm long image inside the camera. It doesn't matter what size the sensor is. The reason you might need a macro lens is that a lot of lenses won't let you get close enough and focus close enough to actually acheive this. That's why a 50mm macro and a 50mm standard lens won't be able to do the same magnification. And THAT'S what I meant by magnification not really describing the lens directly. It's a secondary property and doesn't necessarily tell you much.
That's also why others above pointed out what you might be thinking of - that a 50 mm lens approximates the human FOV on 35mm film or an FX sensor. That doesn't at all mean the magnification is 1:1.
I'm also not sure what you mean by "touchstone focal length" or "by which all others are measured". Focal length isn't a ratio or a comparison value - the focal length is literally a physical property of the lens. It translates directly to a FOV, but not necessarily to a maximum magnification, because that's dependent on some other factors. And that's why I typically ignore magnification - I don't usually care what physical size an object shows up as on my sensor, I just care how much of the frame it fills for the composition I want.
In 4x5, 150mm is approximately the same as a 50 mm lens in 35 mm based gear (digital or film). So under your system, is this a 3:1 lens or a 1:1 lens? You can rig up a LF back to use your 35 mm based body. If you start with a 150 LF lens, is it still a 3:1 lens? 1:1? 1:3?
But 4x5 has different proportions than 35, so is a 135 mm or a 165 mm a better normal lens equivalent? I've seen both argued.
And how about something really odd, like 6x24?
As it currently stands, everyone knows what a 28mm lens looks like through the viewfinder, 50 mm, 100 mm, etc. Also, most photographers, once they have gone through a discussion on magnification, understand that 1:2 is half life size on the recording medium and 2:1 is twice life sized. This is a universal through the camera world. Changing that, especially being so far removed from the origins of the system (from equipment that predates 35 mm by a century or so) doesn't solve any problems that currently exist.
There are all sorts of things that complicate that optical principle which is based on a 'simple' lens. Things like modern lens design which uses multiple lens elements to bend the light rays in different ways creating lenses which are physically shorter than their optical characteristics would indicate. An easy example of that is the + diopter or "close up" lens which, like a pair of reading glasses, allows the lens to focus closer without moving the lens farther out. Like wise zoom lenses use moving internal elements to alter the angle of view.
Without a focal length we would not have the f/stop which is nothing more than a fraction. f/16 for example has a diaphragm diameter of 1/16th the focal length of the lens. Because the diameter is derived from the focal length of the lens f/16 on a 100mm lens is a larger opening than f/16 on a 50mm lens which in turn is larger than the opening on an 18mm lens but... the amount of light reaching the image plane at any given f/stop is equal for all focal lengths. That is due to the law of inverse squares which is a whole 'nuther discussion and I can see everyone's eye's glazing over already.
Yeah, I'm a techie. OTOH being a technical photographer means I understand what's going on under the hood and that is helpful to understanding how we got to where we are.
Is the nodal focal point to film plan a measure of "wideness"??
From memory I think my Nikkor 28 mm is about 71 degrees in width. Other lenses have a "width" also but I don't know the specs. Is there a relationship between focal plane distance and width?
If so, would not that also be a form of magnification?
I've done some astrophotography and telescopes are rated by 1) aperature, which is the lens diameter for light gathering, and 2) focal plane distance. The higher the number the greater the magnification. There is no diaphragm to change the f/number. I guess that function might fall to the occular lens???
A telescope is just a fixed aperature lens and the occular is basically rated in millimeters for additonal magnification of a portion of the image.
Now, a camera attached to a telescope records the image at the focal plane distance. When extension tubes or Barlow lenses (2x) are attached, the focal plane distance is increased and so is magnification. There has to be a mathematical relation to this.
And in microsopes we speak of magnification (diameters), not millimiters. My microscope has 4 objectives and a 10 power occulars (binoc). So I get from 3.5, 10, 40 and 100 x objectives a total magnification of 35x, 100x, 400x, and 1000x. To me this just makes more sense than speaking in terms of 'lens nodal point to film/sensor plane'.
I understand that tradition allows us to be comfortable with how we use these numbers. I'm just asking if my statements are true, which most info coming in says no, but if they were/are, then I would like a magnificaton number. I'm always comparing to binoculars.
And thanks for the time you've spent. I'm archiving some of the replies.
the fisch
The reason it's directly related to FOV is that it's defined by the percent of the FOV that something appears to cover. So if the moon is 2 degrees of view in the sky with your eyes, and 30 degrees of the view in the eye piece, you have a 15X scope. But that works because the earth is essentially a fixed reference to what's in the sky. You can't switch your telescopes focal length, move it closer to the moon, and still acheive the same magnification like you can with cameras. That also means that magnification with telescopes is related to your viewing of it (the "medium") whereas the definition for a camera is medium independent. And cameras magnification varies with focus distance and camera-to-subject distance. I'd imagine this is so much less variation on a telescope it can be ignored.
There is no fixed reference with cameras. I can have a 100mm 1:1 magnification camera lens at 2m from the subject, or a 50mm 1:1 magnification lens at 1m from the subject. Just knowing that my lens is 1:1 wouldn't tell you as much as knowing that it's a 50mm or a 100mm, since that also determines the perspective/FOV.
There are some similarities, and you're right, if you play with the numbers there are relationship's between FOV, focal length, magnification - either camera or telescope definition - and probably a relationship between the two definitions. (Something like 15X telescope is the same as a 1:4 camera lens magnification - you just can't get close enough to the moon to actually get 1:4....something like that anyway, I haven't looked up any equations.) Maybe a good practical optics book would make for a good read. I don't have any suggestions there though.
Addendum/correction: Field of view varies with the design of the lens too. Within any format the field of view varies in the manner I mention above however, a 300mm lens designed for 4x5 necessarily has a much broader field of view than a 300mm lens designed for 35mm film. In that sense it is a measure of a given lens which is not entirely dependent on its other characteristics.
An example : pretend you have an FX ("full frame") camera, DX ("APS-C" or "1.5X") camera, and 300mm lens. If the lens image circle just barely covers the FX sensor, the FOV is about 8.25 degrees, and the image captured will be 8.25 degrees corner to corner. Switching to a DX camera, the same lens creates exactly the same FOV inside the camera - about 8.25 degrees. But what changes is the amount of that FOV captured - it's much smaller. So a DX camera would capture about 66% of the FOV, meaning about 5.5 degrees. This is what creates the focal length multiplier common to digital cameras. The same 300mm lens is :
300mm, 8.25 degree FOV on FX
300mm, apparent 450mm (often referred to as "35mm equivalent" or "mm-e"), apparent 5.5 degree FOV on DX
Thinking about this some more, there are cases where I'm not sure if actual focal length/FOV is used to name the lens, or an equivalent focal length is used to name the lens. Something like Canon's tilt-shift lenses create a much larger image circle than what's actually captured (to accommodate movements). So when we reference, for instance, the 24mm Canon TS-E lens, I wonder if the max image circle inside the camera is 24mm, or if 24mm is just what's captured on the sensor. If it's the latter (and I suspect it is) then that's actually 24mm-e, and the image circle is a wider FOV and shorter focal length.
Angle of view is related to the focal length and the film size. It works like this:
a = 2arctan(d/2f)
a is the angle of view
f is the focal length
d is the film dimension (horizontal, vertical, or diagonal)
Jim and David, I think you're conflating angle of view and angle of coverage. The angle of coverage is the angle of the cone of light coming out the back of the lens. The angle of coverage determines the size of the image circle. It's independent of the film size and focal length.
In David's 300mm lens example, the angle of coverage stays the same but the angle of view drops from 8.25 degrees to 5.5 degrees because the film size changed.
To help pull all this together I'll give another example. I have two lenses right in front of me. Both are spec'ed at 150mm focal length and f/5.6 maximum aperture. One has an angle of coverage of 72 degrees, the other is 105 degrees. The 105 degree lens has a huge image circle compared to the 72 degree lens. Both of these lenses will produce the same angle of view on 4x5 film - about 45 degrees on the horizontal (5 inch) side. And both lenses will cover 4x5 film with lots of room for movements.
On 8x10 film a 150mm lens will produce an angle of view of about 90 degrees on the 10 inch side. Notice that the required 90 degree angle of view exceeds the 72 degree angle of coverage of one of the lenses. That lens will not cover 8x10 because it isn't capable of projecting a 90 degree angle of view. Trying to use the 72 degree lens on 8x10 would result in severe mechanical vignetting - I would get a round image that didn't fill the entire sheet of film. The 105 degree lens covers 8x10 quite nicely, thank you very much.
So what about digital?
It's exactly the same. In terms of optical principles, digital sensors are just electronic film.
Getting back to Larry's original question, lenses are spec'ed by focal length because that's a physical property of the lens. Things like magnification ratio and angle of view will vary depending on how the lens is being used.
The really fun question, the question that keeps me up at night is: How do they make a zoom lens with a constant maximum aperture?
Think about it. I have a 28-70mm f/2.8 lens. At 28mm the maximum aperture is 10mm. At 70mm the maximum aperture is 25mm. How do they do that?
Pop! Fzzzzt!
Drat! there goes that fuse in my brain again.
Cheers,
Mark
The angle of coverage is intially started by the lens. A lens with a large angle of coverage must have a short focal distance. If one could observe the light behind in the lens, say in a very dusty room, the angle formed by the light approaching the focal point would be the angle of coverage. The size of that spot is determined by where the film/sensor is placed within that cone of light.
The focal point of the lens does not change. It is a physical property of its glass and design. Yet in a compound lens the focus can change.
Now for the statements and questions:
Is the film/sensor plane at the focal point? Or is it manipulated by the focusing ring on lenses to maintain focus at the film plane? It would seem so but I keep thinking of my days as a child playing with a magnifying glass. The focal point of the sun directed through that glass would burn paper but it was a very small spot. The bigger the lens on the magnifying glass the hotter the focal point because more energy was passing through the lens. In terms of photography that would be a "faster" lens.
Now, again, is the focal point where the maximum energy in terms of light is placed on the camera or can film/sensor be in front of that focal point or focused in front for a larger circle of coverage? Is/can "focusing" the lens change any of this? I realize we are dealing with compound lenses and that probably adds major complications in my kid's toy.
Thanks for everyone's time. I'm learning-------I think (arc tangents !!!!!???? long time ago for me)
the fisch
That's the part that I didn't understand. I was originally assuming that a 300mm lens for 35mm will always have the same angle of coverage (I suppose you could call this the lens FOV, as opposed to the camera or sensor or image FOV) - until I realized that the tilt-shifts can't have the same angle of coverage.
So here's what I'm still wondering - and maybe someone can help. How is lens focal length specified for a lens? Is it the apparent focal length based on 35mm film? Or is it the true focal length which directly translates to angle of coverage, which is format independent?
I think it must be apparent focal length, since, as I mentioned above, a 24mm tilt-shift must have a larger angle of coverage than a 24mm standard lens. Therefore, 24mm is just the equivalent focal length based on 35mm film or a full frame sensor.
Right? And is that true of all lenses?
As I explained earlier the focal length is the distance from the the focal point to the optical center of the lens when focused on infinity. If your subject is closer you must move the lens further from the film/sensor plane. The focal point changes with the distance to the subject but the focal length of the lens does not. It is a fixed unit of measurement based on focus at infinity.
As you focus on things closer and closer the amount you have to move the lens away from the film/sensor increases in inverse squares. Focusing on something at 30 feet vs infinity requires a tiny movement whereas focusing on something at something at 3 inches vs 3 feet requires a much larger movement of the lens. Since light falls off in inverse squares as well this means that the physical opening of any particular f/stop results in less light falling on the film/sensor than the number indicates. Modern lenses for digital and 35mm compensate for that within the limits of design but those limits are why you will see zoom lenses rated f/3.5-4.5 or similar. The lens design does not allow the diaphragm to open enough to fully compensate when the lens is at its maximum extension so the actual value falls from 3.5 to 4.5.
Field of view is how broad an angle the lens sees (the angle in front of the lens). Field of coverage is how big the image circle is on the back side of the lens. Both vary with the design of the lens. A 65mm lens on a 35mm camera is nearly normal in its field of view but a 65mm lens for 4x5 is very wide angle. However if you put the 65mm lens designed for 35mm on a 4x5 camera its field of view (and coverage) would still be the same as it was on the 35mm and you would only get a small circular image in the center of the 4x5 film. There is an excellent demonstration of this by Ansel Adams on page 61 of BASIC TECHNIQUES OF PHOTOGRAPHY by John Schaefer. I highly recommend that book.
Good stuff. I'll visit your old website.
I think one item that I've not considered is the "focus" power of the lens compared to a magnifying glass.
I understand circles somewhat and the relation of "inverse squares".
Now, is the FOV the same regardless of focal distance, ie infinity or 3 feet.?
I would presume that at full aperature it would be the same because the angle of light falling onto the focal plane must be the same at a given aperature or with a specific lens. That feature, as was explained before, is inherent in the lens. It would give the same field of coverage.
the fisch