Preface: I worked on the following article over several nights. It's rough, repetitious,and wayyyy too long. I've included stuff that ought to be edited out, but what I tried to do as I wrote this was to shed some light on a few differences between APS-C and larger format cameras, like 35FF or 120 roll film in either 6x6 or 6x4.5 format. So many people are unaware of what HFD or hyperfocal distance means, and are unaware of how DOF does not respond "equally" or in a linear fashion. I often read facile rule of thumb comments that say one needs only 1 and 1/3 stops wider an aperture when using an APS-C camera to get the "equivalent depth of field" of a 35FF format camera. A little bit of research will show you that achieving "equivalent depth of field" between APS-C and 35FF is sometimes *impossible*. As in, *impossible*. The differences between formats can be worked both ways too--it is not a one-way street,and I am not attempting to advocate that 35F is "better" than APS-C, but it is DIFFERENT. And at times, there is *NO EQUIVALENT* attainable between APS-C and 35FF. Please, take note: I am not saying the increased DOF per angular view of APS-C is better than the decreased depth of field per angular view of 35FF--but it is different. In a shorthand way one might say that landscapers love the deeper DOF, and portrait/fashion/studio people realize the APS-C format is perhaps a bit too small a format for the ultimate in versatility, and that APS-C in many situations pushes their images too much toward the deep DOF end of the spectrum.
The web is full of people who have never studied optics or lenswork,and who have a never made photographs with a 4x5 or 120 camera,and who thus really don't have any REAL experience with what it's like to work with a format that is distinctly different in size and pictorial rendering than the much-smaller 35FF or APS-C formats. If all you've ever shot with is an APS-C fomat camera, it's probably impossible for you to imagine how RESTRICTIVE a 120 rollfilm SLR is when you want to try and get deep depth of field using the normal 80mm lens. Shooting in 6x6 format with the normal angle of view 80mm lens set to f/8 and focused at 10 feet, DOF extends from 8.57 feet to 12 feet, for a total DOF band depth of 3.43 feet. Using an APS-C camera with a 31.4mm lens, focused at 10 feet, at f/8, DOF extends from 6.83 feet to 18.7 feet, for a total DOF band of 11.9 feet.
Ponder this: a 6x6 camera will yield a depth of field band that's LESS THAN three and a half feet deep at f/8 at 10 foot focus. But, if you put down the 6x6 format camera and pick up an EOS 20D with its zoom lens set to 31.4 mm, that format will pull depth of field from 1.75 feet closer than would the 6x6 format camera. Where the 6x6 format camera gives a shallow 3.43-foot deep DOF band ,the smaller EOS 20D gives a solid,expansive 11.9-foot deep band extending out to almost 19 feet, while the 6x6 Bronica would cut off sharp focus at 12 feet. To recap,the 6x6 medium format camera gives a DOF band of 3.43 feet, while an APS-C camera gives a DOF band that's 11.9 feet deep when both cameras are fitted with the "normal" lenses for their respective format sizes and focused at 10 feet.
I can assure you I studied these issues,a long time ago,and what I've tried to write is based on both science and practical,as in 'actual pictures made' photography experience with 4x5,120,35mm film,and APS-C digital cameras. About 34 years of shooting, first with 620 rollfilm, then with 35mm adjustable camera in 1974, then 120 rollfilm TLR cameras which used to be cheap and plentiful,and most recently and finally almost exclusivly with APS-C digital SLRs.
The Atkins article gives this rule-of-thumb comparison of depth of field between APS-C, 35FF,and 6x9 rollfilm at "moderate focusing distance" . If 35FF has a depth of field value that is 1.0, then APS-C brings roughly 1.6x MORE depth of field than 35FF, while 6x9 cm rollfilm capture brings only 0.4 as much DOF as does 35FF. So, to reiterate,the numbers are 1.6x, 1.0, and 0.4. APS-C has more DOF than 35FF by a factor of 1.6x, and 6x9 cm has less DOF than 35FF. This only holds true at moderate focusing distances which are well below 1/2 of the Hyperfocal Distance. Beware of the carefully-constructed comparison photo "example" seen in a popular web article showing "equal" depth of field at a distances of about 1 meter,using some small models on a monopoly board. YES, it's possible to go to The Luminous Landscape and see a carefully-constructed sample photo showing a small-sensored P&S digicam and a 1.6x Canon's output,with "equalized" depth of field and identical angles of view, with close-range focusing showing very similar image characteristics. The problem is, the sample photo's situation has been cherry-picked,and the focusing range has a background distance of probably no more than 1.2 meters...there's no distant background to see,and the depth of field characteristics at CLOSE range shift dramatically as the focusing distance moves out toward even 2 meters; with the tiny-sensored-cameras, once your focus distance gets out into even moderate distances like 2.5 meters, your pictures will almost ALL have depth of field that rapidly extends right to infinity,meaning that almost ALL normal scenes will be to state it plainly, "deep depth of field scenes".
The LL article shows that equally-deep DOF can be had with a point and shoot and a small-sensored d-slr; yes,true. But the example does not address focusing at distances approaching hyperfocal distance, NOR does the example show a _SHALLOW_ depth of field comparison, since no parity can be achieved, hence my use of the term cherry-picked. The article I obliquely reference is typical of the academic type of half-truths so many web-published articles point out. The use of the Monopoly board is funny though!
There is no "Lens Magnification Factor" with APS-C. You're using an entirely different FORMAT when you use an APS-C camera. A 100mm lens projects the same size of image on an APS-C body as it does on a Full Frame body, but on the APS-C body, the edges of the lens's image circle are cropped off. Re-read that sentence again if you need to. A 100mm lens projects the SAME SIZED image on an APS-C body as it projects on a Full Frame body. The magnification of the 100mm lens is the same, no matter if the full image circle of the lens is captured, or if some of the circle's periphery is cropped off and not captured--the magnification of the subject with a 100mm lens is the SAME, no matter what format or size of sensor catches the light rays!!! That is a FACT! However, there are many people who say that an APS-C sensor "magnifies the image" of each lens mounted on the camera and in that contention they are WRONG; all the APS-C sensor does is to record only the center portion of the lens's projected circular image. I know that fact is hard to believe for many. But it's true. There is no Lens Magnification Factor when using a crop-sensored d-slr.
APS-C is a different FORMAT than is 35FF. Many people have insufficient experience with formats other than APS-C digital,and thus they fail to understand why,or exactly how, the various formats DIFFER from one another in real-world picture-making scenarios and how different formats bring different "looks" to their pictures. Keep in mind that MUCH of what you read on popular internet photography forums is incorrect,and when the subject turns to lenses and optics, MOST of what passes for fact on today's internet is only half-truth at best.
PART 1: Different Formats Behave Differently In The Real World
Format size matters a LOT in terms of depth of field performance. Those who have shot 4x5 sheet film, 120 rollfilm, 35FF, and crop-sensor d-slr's can appreciate, from their OWN experience how larger format and smaller format cameras perform very differently in the real world. Those who have shot large format, medium format, and 35FF know, from actual experience, that moving to a smaller format camera brings with it greater mobility, lighter weight, and shorter lens lengths in all categories; as format size gets smaller, wide angle,normal,and telephoto lens lengths can be made shorter and shorter and shorter. Those who have actually shot multiple, different formats will tell you that one of the single largest differences between large,medium,and 35FF formats is the difference in image "look" due to depth of field differences and lens performance characteristics between the three formats. Until you've actually shot large,medium,and miniature formats (4x5, rollfilm,and 35FF) then you're probably not truly experienced in how the size of the your camera's capture format affects the way the camera records images using lenses,and how format size affects the photographic process. Sometimes, it's a matter of nuance between what two formats can do better,while at other times using the wrong format of camera can make it almost impossible to get what one wants to achieve,pictorially-speaking.
I have shot 4x5,120,35FF,and APS-C,and currently own cameras of all four formats. I happen to own a Fujinon 150mm f/5.6 lens for 4x5 which is my main 4x5 lens; I own a Bronica PS 150mm lens for use with both 6x6 and 6x4.5 film backs, and I own a 75-150 Nikon Series E lens which I used a LOT on 35FF,and have also used the 150mm focal length quite a bit on APS-C Nikon and Fuji and EOS 20D bodies. My Bronica medium format slr could be consider a three-format camera: I have multiple 6x6 and 645 backs for it,and I also have 35mm panorama back for Bronica SQ. I bought into the Bronica SQ line of camera bodies and lenses in the early 1990's because I did not want one of the many slightly-smaller,slightly lighter 645 rollfilm SLR cameras that were popular then, but I instead wanted a rollfilm SLR camera that could shoot BOTH 6x6 and 645 format images,using the the same lenses but with different rollfilm backs for each format I wanted to shoot in. Different formats have different uses. Having three lenses, 65-80-150 and two rollfilm capture formats made my Bronica SQ investment more useful to me than just buying a 645-only camera like a Bronica ETRs or a Mamiya 645 or the Pentax 645. Plus, the Bronica SQ 645 backs I bought for the SQ series bodies capture their images in a vertical orientation,not a horizontal one. The 645 format is nice for portraiture,since so many shots will look best as vertical compositions.
To those who ask what DOES a larger format do to the pictures? Let me try and give you a short answer. The smaller the film or digital sensor capture size, the more you can get in-focus using normal f/stops like let's just say f/8. With a large camera like a 4x5 using a normal length lens at f/8, there is not very much depth of field either in front of or behind the focus distance. On 4x5,you'd better be thinking f/32, not f/8 if you want much DOF. Moving downward in capture size,you'll find a 75 or 80mm lens is standard for 120 square rollfilm pictures. Shooting with a 35FF camera and its normal 50mm lens gives you deeper DOF than does a rollfilm SLR with its 80mm normal lens. 35FF is a nice format, one that allows both deep, AND shallow depth of field compositions with a huge array of EXISTING lenses. 35FF is a format that's been fully exploited by the camera and lens companies for around five decades; APS-C is a new format,and the majority of the time we are using lenses designed for 35FF use on our newfangled APS-C cameras,and that's not all peachy-keen.
The reality of shooting with any brand's APS-C cameras is that the normal angle of view lens is a relatively SHORT focal length of only about 31 millimeters. With a 31mm normal lens set to f/8, an APS-C format camera will deliver a HUGE amount of depth of field. Simply a HUGE amount of inherent depth of field,ready to come out as soon as the focusing distance stretches out a little bit longer than a big sectional sofa's length. Notice how I said an APS-C camera will "deliver a HUGE amount of depth of field"? Please take note; if you want deep depth of field, APS-C delivers deep depth of field in a big way: as much as 1.6 to 1.9 times, to as much as 2.85 times MORE depth of field than 35FF delivers, with the SAME angular field of view,using the example lens of a 31.25mm lens on APS-C and 50mm on 35FF. The amount "more" DOF APS-C yields is dependent upon how close the lens is focused in relation to the hyperfocal distance for the focal length in question.
You can look at the APS-C camera's delivery of deep DOF as a positive in some cases. In other cases, with other subject matter, deep DOF might not be wanted and might be seen as a negative. In landscape photography, deeper-than-35FF depth of field with apertures like f/8 on a top-grade camera like the Nikon D2x is pretty nifty. F/8 is not diffraction limited on the D2x, and f/8 and a smaller image shot with a 35mm lens will get you MORE depth of field than using a 35FF camera and a 50mm lens. In people photography,however, APS-C has a disconcerting tendency toward being on the side of creating too MUCH DOF in real-world photo studios and living rooms and outdoor locations, and I am not saying this to be negative, but there are BIG,real,observable differences in the "look" between APS-C and 35FF cameras when used for many "people photography" situations. It's not that APS-C is useless for people photography,and that 35FF is Nirvana, but the truth is somewhere in between.
Now, if you've ever struggled to pull deep depth of field from a landscape on 120 rollfilm, you've run into the need for something along the lines of f/32 at which depending on time of day and film speed might mean exposures as long as 1/2 to 3 seconds. That LARGER FORMAT 6x6 camera's capture area and its 80mm normal lens needs to be stopped wayyyyy down to pull anything resembling deep depth of field. Frankly, 645 makes some sense to me as a landscape format if you want deeper depth of field,especially if your camera is set to shoot horizontals easily. The smaller area of 6x45cm versus the 6x6 square gives you the ability to get a little bit more depth of field,at either larger f/stops, and/or higher shutter speeds,plus its relatively large capture format gives better detail than 35mm film can.
APS-C's small physical size means your wide-angle lenses must be very,very short focal lengths. Shorter focal lengths bring deeper and deeper DOF. As one down-sizes the capture format, the hyperfocal focusing distance of each focal length of lens grows shorter and shorter. Go to the on-line depth of field calculator,and look up for yourself the hyperfocal distance for a 50mm lens when it is used on an APS-C body and when the SAME lens is used on a 35FF body. One downside of APS-C is the need for wideangle lenses in the under-18mm range, which necessitates complicated,costly,aspherical lens designs to get rid of geometric distortion that's pretty easy to avoid even when using non-aspherical designs on longer lenses on the larger 35FF format. So, APS-C necessitates more sophisticated,costly,and hard to make aspherical wide angle lens designs,which is not as big a problem as when the capture format is larger. 35FF's larger capture size means that any given wide angle focal length will show a vastly wider angle on every scene than that same lens will show on any APS-C camera. A 14mm lens encompases an angle of view that's a hell of a lot "wider" on a 35FF camera than it is on an APS-C camera.
Many shooters find themselves being forced to move farther away from subjects to compensate for the APS-C sensor's cropping off of every lens's imaging circle. Increasing camera-to-subject distance is the first,easiest,and best way to increase depth of field. The short focal lengths needed on APS-C bodies,and the closer hyperfocal distances due to the APS-C format's smaller size relative to 35FF both,in concert, work togehter to help boost depth of field on APS-C photographs. The common use of fairly short focal length settings on APS-C cameras, combined with the increased camera-to-subject distances together make it almost *impossible* to create anything even remotely resembling a shallow depth of field "look" with an APS-C camera and a wideabgle lens. APS-C is a capture format that is either cursed or blessed with deep DOF,depending on how you want your images to look,and on what "looks" you wish to be able to create. 35FF offers a good mix of "looks", and the lenses to create these various looks are all in existence,right now,today; the same can NOT be said for APS-C format cameras--this format has been in existence since 1999,and as yet,not all the lenses needed have been made for APS-C, and many never will be made.
The APS-C lens needs to deliver high spatial frequency information to a small,densely-packed sensor that needs a 28mm diameter image circle. The 35FF format uses a 43mm diameter circle of coverage from the lens,and depends more on good edge-to-edge performance across a larger image area. Put a 100mm lens on a 35FF camera or an APS-C camera,and the SIZE of the image projected will be the same on both cameras, but the outer portions of the 100mm lens's image circle WILL be recorded on an EOS 5D,while the outer edges of the len's 43mm image circle will NOT be recorded on a 20D body.
APS-C has taken photography one step closer to the ultimate in the consumer snapshot ethos,which was a Kodak invention called the Disc format. Kodak engineers knew that with even 126 and with the even smaller 110 film format cameras, that the film formats of 126 and 110 were both too LARGE to allow for a good,motion-stopping shutter speed with a small enough f/stop to provide hyperfocal depth of field deep enough to get into the 2.5 foot to infinity range using ISO 100 or 200 film. Consumers using 35mm FF, 126, and 110 were STILL getting out of focus blobs when people got too close to the camera. Kodak engineers undertook the task of eliminating out of focus close-range subjects,permanently, by shrinking the film format smaller than had ever been offered for a mass-market camera (ie not a "spy camera" like a costly Minox or Tessina,but a Grandma-and Mom-affordable camera). Kodak designed and invented and built millions of Disc cameras,which due to the ultra-small format needed an ultra-short lens for a normal angle of view. Consumer digicams with the smallest of sensors...well, there's the disc format concept of small capture size/deep DOF/not much need for critical focusing coming back with a sensor instead of a rotating flat cardboard disc with film catching the light rays from that teensy-tiny little lens!
The small format and short focal length lenses used by the ultra-small Disc format cameras meant sharp focus from about 2.5 feet to Infinity. The Disc format cameras were all focused at their hyperfocal distance at the factory,and therefore there was never any need to focus! It was ALL in-focus! Woo-hoo! With the Disc format, it was * impossible* to throw the background out of focus. The Disc format was based on the NEED to create a film format physically small enough to allow a very short focal length lens to be set to hyperfocal focusing distance,and thus to eliminate the need for ANY focusing on the part of the end-user. *Everything* would be in focus,even pretty doggone close-up grand babies,and kitties,and flowers. The diminutive capture format,and its neccessarily short focal length lens meant that Kodak engineers had created a no-fuss, no-worry,foolproof picture making machine. And they did it by boldly going much SMALLER than even 110 format's postage stamp sized negative and dropping all the way down to a capture size that's in the size range of what today's cheap digicams use,to get THEIR deep depth of field off of small format captures. Brilliant Kodak engineering. And the underlying basis of today's small-sensor digicams. A little history lesson there.
35FF allows you to throw the background out of focus with truly fast wide angle lenses, with all normals, and with all telephotos. AND it allows you to pull reasonably deep DOF too,if you'd like that. But APS-C shifts the capture size smaller, bringing deeper DOF with every angle of view equivalence. This is what new shooters seem to miss; a significant change has occurred in the shift from 35FF to APS-C cameras,and it's not just about "equivalent focal lengths". It's about lenswork. And capture size. It's about tools,like lenses,and how they actually WORK in places like basketball courts,track and field and soccer fields,portrait studios,and on-location in all types of situations. The hallmark of professional portraiture, a sharply-rendered sitter or group, with an out of focus and a truly non-destracting background has been hurt pretty badly by the APS-C shift. Due to the way optics rears its ugly head, Nikon and most other manufacturers have not made wide angle lenses with maximum apertures wide enough (like f/1.4) to compensate for the increased DOF the smaller APS-C cameras deliver. So far, most camera makers have only produced f/4 wide angle lenses, and in some cases f/2.8 wide angle lenses, but what would be actually needed to overcome the smaller capture size would be some wides with apertures as wide as f/0.7 or f/0.8, and 70mm-75mm lenses as fast as f/1.2. Such lenses are nowhere to be bought,and might never be manufactured.
ULTRA-Important FACTS To Remember: DOF increases HUGELY as the focusing distance approaches the hyperfocal distance. The smaller the capture format,the sooner the lens will get to hyperfocal distance. Consider that once your format gets small,like APS-C small, there's a tipping point where even though objects are out of focus,and beyond the stated depth of field band,that those objects still have ample visual clarity to identify and to draw attention away from the foreground subject. The inherently SMALL capture size of APS-C format, and the combination of necessarily short focal length lenses like 18 to 50 mm lenses means that using a lens as long as 50mm on APS-C, you can shoot photos of people who are only 2 to 3 meters away,and even at f/5.6, the background 45 feet behind your subject will actually be rendered in-focus-enough to be somewhat distracting. The downward shift in focal lengths needed to make wide-normal-and tele lenses on APS-C format camera brings us right up to and then takes us past a "tipping point"--a point where we often find that there's MORE depth of field than we'd really like to have. This is the area that a careful analysis of my own photos has made me conclude I simply had to get back to full frame capture. This paragraph is perhaps the most essential paragraph to understand in this essay.
Medium format in the form of 6x6 or 12 frames on 120 roll film gives you a lot of room to crop,from a large negative. A 150mm is a moderate telephoto lens on 6x6 format and it feels sort of like an 85mm lens feels on 35FF to me.When you use a 150mm lens on 6x6 it does NOT DO DEEP DOF, not even close to what you can achieve on APS-C with a similar angle of view lens. As one goes larger in capture size, it becomes harder and harder to make pictures that have deep depth of field,unless the lens is stopped wayyyy down, or you use camera movements as on a view camera.
35FF has significantly more Depth of Field freedom than does 6x6 rollfilm. 35FF gives the photographer the freedom to either open up and blow things out, or to stop down and to pull pretty deep DOF. With a 35FF camera and lenses, there are some VERY wide-aperture Canon autofocusing lenses that can make shallow depth of field images,even in the wide-angle focal length ranges like 24mm and 35mm. 35FF can also be stopped down to f/11 or so and deep DOF effects can be obtained. 35FF offers the serious shooter a wide range of options in terms of camera-to-subject distances,angle of view, focal length,close-focusing,and so on. There is no format that has more lenses designed for it than the 35FF format. Canon EF mount and Nikon F lens mounts have several hundred different lens choices available. 35FF can do very shallow DOF work,moderately deep DOF work, and pretty good deep DOF work over a wide range of focal lengths,and there are lenses galore that were designed for 35FF. 35FF has been "king" ever since the 1953 Leica M3 set the standard. Larger and SMALLER formats have been tried, like Kodak's Bantam 135 or 828 format, the cartridge-loading 126 format,and the Half-Frame 35mm format models like the Olympus Pen half-frame series, and two decades later, 35mm Half-Frame models made by Yashica-Contax/Kyocera,with the Yashica Samurai line of Half-Frame 35mm film SLR's. In the late 70's-early 80's there was the faddishly semi-popular Pentax made 110 format single lens reflex interchangeable lens camera,with autowinder and electronic flash options. In the mid-1990's, Minolta pretty much lost its ass on the APS or Advanced Photo System format which they invested very,very heavily into,despite the fact that consumer digital cameras were just around the corner. My wife has a nice Minolta Advantix APS-format film SLR. Nevermind that the APS film format and all its cameras died on the vine because nobody wanted to buy into the all-new format and its at-first scarce photofinishing options due to the multi-format APS aspect ratio choices and the rarity of photofinishing machines that could handle the new film cartridges/archive holders.Even with the beautiful engineering and multi-format selections the handsome and stylish Minolta APS Vectis SLR cameras died out quickly. Sometimes formats do not last long. APS lasted what? Six years from the format's inception to its discontinuation? Something like that? The Disc format is now also dead. Kodak's Polaroid-like formats and cameras....also dead.
35FF uses a different capture size and a different range of focal lengths than medium format. A moderate wideangle lens on 6x6 is a 65mm lens,which subjectively feels somewhat like a 35mm lens feels when shot on 35FF;on 6x6 a 65mm lens is a semi-wideangle lens,and it's always,always, going to be a 65mm lens, and it will not "do deep depth of field" in the same way that a 35mm lens on 35FF camera can "do deep depth of field" shots. The LARGER the FORMAT one uses, the more your camera tends to have a focus band that drops off rapidly behind the point of sharpest focus. For street and PJ work, the 4x5 inch Speed Graphic's format meant it was hard to bridge near and far focus unless small f/stops were used and powerful flashbulbs were used to get to those smallish f/stops,so when the smaller 120 rollfilm cameras got good, most people doing social photography moved to cameras using 120 rollfilm,like the Rolleiflex camera. When film stocks got better, the smaller capture of the 35mm full frame Leicas,Contaxes,and then later Nikons FINALLY became acceptable,and there was a greater acceptance of 35mm camera for reporting and social uses,as well as sports photography.
35mm full frame capture has been a workable,viable format for many uses from the late 1930's until today. 35FF represents a nice format size,with a lot of potential for ultra-wideangle lenses, shallow DOF in wideangle compositions with high-speed lenses, deep DOF in wideangle compositions when stopped down, and relatively flexible background control from 50mm to 200mm using f/stops from f/2.8 to f/11. 35FF is a small format,compared to 6x6 or 6x9 or 4x5, but it can do a lot. MOST ALL of the world's 35mm lenses are designed to work on 35FF cameras.
My first APS-C format camera came into my life in February of 2001,when I bought a Nikon D1. Since then, I've owned several more Nikons and Fujis and one Canon, all APS-C sensored cameras. The biggest difference between 35FF and APS-C is that with 35FF, I have a full set of lenses that were designed and optimized for one format,and one "real-world". With APS-C I have a lot of lenses pinch-hitting in roles they were never designed for. There's a reason the 100 and 105mm lenses were designed. There's a reason the normal wideangles go 20-24-28-35, and a reason why 50mm,85,105,135,180,200,300,and 400mm designs were built; because they work very,very well on 35FF capture cameras in the real world. Using 35mm film-era lenses on cameras with cropped-down sensors is a bit different than merely multiplying a focal length by 1.54 or 1.6x and saying, "Oh, this is my new equivalent lens."
********Part Two-Some Simple Examples of DOF Differences Between APS-C and 35FF Capture Format Cameras**********
I looked around the web to find one,single article that would demonstrate that cropped-sensored d-slr's actually are cameras that represent a different format than the older 24x36mm or 35FF format. Well, I found an article that has some very easy-to-understand charts and a graph and some plain-English explanatory points about how depth of field differs between different capture formats. While an APS-C camera and a 35FF camera might look similar,and can use the same lenses and flashes and accessories, often times the images that come out of the two cameras will exhibit somewhat different looks, to in some cases VERY,very different looks. Aesthetics and intent take more than casual study. Equivalent angles of view do not in any way mean identical images. Far,far from it.
Let's closely examine the third of the colored Depth of Field tables (the lavender colored table). The third table describes DOF behavior using a 1.6x crop sensored Canon d-slr at a focus distance close to hyperfocal distance, with a lens focal length of 31.25mm which will give a 46 degree diagonal angle of view--the same angle of view as a 50mm lens used on a 35FF camera like an EOS 5D or a Nikon F5. So many proponents of cropped-sensored cameras claim that all one needs to do is to figure out what focal length on their cropped-sensor camera will yield the same angle of view as a full frame camera would get, and that everything is peachy keen,and that anybody who complains ought to shut up,a la Bill O'Reilly. Some people even admit that ,"They can't see the DOF issue as being significant." Well, it is significant,provided you have the equipment and the knowledge and the photographic education to understand some very fundamental lenswork concepts. But then, not everybody has shot on three or four film formats, and not everybody is aware of how 6x7 and 6x6 offer significantly different lens choices and DOF possibilities than 35FF offers, and that the difference between 35FF and APS-C is actually a pretty substantial difference. The difference is of about the same magnitude as the difference between 6x6 and 35FF,in my experience.
The EOS 10D's lens is set to f/8,with a 31.25mm focal length setting, the depth of field for this cropped-sensor camera is from 2.85 meters near point, to 20 meters far focus, for a depth of field band of 17.15 meters, or 2.85 times more DOF than a 50mm lens on Full Frame. With the 50mm lens on a Full Frame Body, an f/8 lens aperure and the 50mm lens focused near its hyperfocal distance,10.6 meters, the picture will have a depth of field with near focus from 3.4 meters, but extending back to only 9.4 meters, for a depth of field band of 6.0 meters.
So,let's recap: Using an APS-C Canon using a 31.25mm lens set to f/8,focused at near hyperfocal distance, we get depth of field from 2.85 meters to 20.0 meters (a DOF band depth of 17.15 Meters.) With a Full Frame body and a 50mm lens,set to f/8 and focused near its hyperfocal distance,we get depth of field from 3.4 meters to 9.4 meters (a DOF band depth of 6.0 Meters). Same angular field of view between the APS-C body and the 35FF body,right? Yes,right. But a tremendously DIFFERENT depth of field and image rendering.
Using a 1.6x cropped sensor camera, the hyperfocal distance of a lens is 1.6x closer than with that same exact lens deployed on a 35FF body. Again,re-stated slightly differently,the smaller capture area of APS-C shifts the hyperfocal distance of a given LENS 1.6 times CLOSER than when shooting that same LENS on a 35FF capture medium,either film or sensor.
As Atkins says in explaining this third chart "Between about 0.2m and 3m the 10D shows about 1.6-1.7x the DOF of 35mm film. At very close distances the ratio goes up, and as the distance approaches the hyperfocal distance for a 31.25mm lens at f8 on a 10D (6.6m) the ratio rapidly rises - this is because the DOF behind the subject in the 10D image is rapidly moving towards infinity."
If you go and read this Bob Atkins article on depth of field, and really take the time to understand it, you'll find out why I think depth of field control issues and background control issues are so problematic on APS-C cameras,especially as lens focal lengths dip down into the under-60mm range. Take very careful note of how the difference in depth of field goes from roughly a steady 1.6x to 1.7x greater with an APS-C camera compared with 35FF, to as much as 2.85x greater depth of field when the focus ring is set to something as simple as 6.6 meters at f/8 with a zoom setting of 31.25mm...the depth of field band goes waaaay out to hell and beyond on an APS-C camera. However with a 35FF format camera, the depth of field band is six meters, or roughly 18 feet total...but the cropped-sensor APS-C camera yields a DOF band that is 17.15 meters or roughly 53 feet deep! The practical,real-world implications of dropping sensor size below 35mm and down to APS-C are pretty clear once you start looking at the focal lengths and the actual optics involved. Unless you've actually seen how OUT of focus you can render a background and still create a true wide-angle composition from a distance of less than 15 feet on 35FF, you can hardly appreciate what the small format of APS-C brings to the table,which is inherently DEEP depth of field,readily and easily. Too much depth of field sometimes. On APS-C you hit hyperfocal focus distance that's about as far as you can spit,and then your fancy camera and costly 12-24mm zoom lens has been turned into almost the equivalent of the 110 format. APS-C and a wide lens yields so much depth of field that you feel like a member of the f/64 Group (look it up if you must). And, with APS-C your studio backgrounds will all tend to be just a hair too much in-focus if you're not incredibly vigilant. In-studio work in front of paper and muslin bckgrounds is one area where APS-C cameras fare badly in many situations.
If you cannot understand the lavender colored chart found at http://photo.net/learn/optics/dofdigital/ in real-world,practical terms, you need to re-read it,look it,and strive to understand that the 46 degree diagonal angle of view covered by an APS-C camera with a 30mm f/1.4 Sigma lens and by a 35FF camera using a 50mm f/1.4 lens will produce significantly different images under many circumstances. Note that all smaller film formats achieve hyperfocal depth of field earlier,at closer ranges. The problem with APS-C is two-fold; you either zoom the lens short to get a full figure person in, or you move the camera farther back than you'd normally stand using a 35FF camera,so as to compensate for the narrowed angle of view the sensor sees when using your 35,50,85,105,or 135mm lenses; either way, you'll have deeper DOF with an APS-C camera than with a 35FF camera with the same picture angle of view. The smallest commercially successful film format, the Disc format, was designed specifically to give the deepest possible focus,with the closest possible hyperfocal distance. How? By making the smallest capture format film camera ever sold in quantity. Optics at work. Small format. Small,short lenses to cover it. Deep depth of field even at modest aperture like f/4.5. No need for focusing. Ever. Once an optical system's capture format gets very small, the NEED, the necessity for critical focusing largely goes away,and a simple "Set it to 1 meter and forget it" type of intrinsically DEEP depth of field is created by virture of 1) a tiny capture size and 2) a short focal length lens.
On a continum, APS-C is much more on the side of the DEEP depth of field formats that have existed over the decades, while 6x6,6x7, and 6x9 rollfilm cameras represent the most common "Shallow depth of field" formats that have been popular to any real extent over the last few decades. As the British say, "Horses for courses." As in,different horses for different courses. I wouldn't expect a plow horse to win a stakes race,nor a Kentucky Derby runner to be able to help pull like a plow horse in the lower 40 acres.
When you shoot with an APS-C format camera using its very short wide-angle lenses,you will be shooting at close to hyperfocal focus distance at even moderate distances,thus making it almost impossible to create a wide-angle picture with significant foreground/background separation. The APS-C format's smaller capture size,shorter focal lengths, and increased shooting distances plays havoc with the principles of foreground/background relationship and subject isolation.But,by using a larger camera format and its correspondingly longer "wide angle of view" lens,it's possible to show a human figure full-frame,with a wide angle of picture view,from close range, and to throw the background OUT of focus. And that is the major difference between large,medium,minature,and APS-C,and ultra-miniature format cameras; as formats get smaller, we need progressively shorter lenses. By the time the format has gotten as small as APS-C, the increased DOF is so profoundly more that we've moved into an entirely new type of imaging: APS-C brings with it deeper depth of field than 35FF,and loses the "balance" between shallow DOF and deep DOF choices that gave the 35FF format about 50 years' worth of good,solid service.
David Burnett has recently begun covering high-profile news events,like Washington, DC congressional hearings, the Olympics,and so on using a 4x5 Graphic. Have you seen the pictures? Do you see how different they LOOK,compared to what everybody else is shooting on 35mm or smaller? Big,big difference. Due to format size and lenses.
Science, not opinion. Go to the library and look at Life magazine from 1945,when the predominant format was 4x5 inch, not 35mm FF; those photos from 1945 have a look that's very decidedly different from "miniature format" photos made on 120 rollfilm or 35mm full frame film.
The facile idea that one can simply do some quick math and "convert" lenses from one format to another format without substantially altering the imaging characteristics does not hold water. The mistaken idea that "equivalent angle of view equals same picture" between 35FF and APS-C formats is patently wrong. Sure,you get the same angle of VIEW--but the pictures are very,very different. Even though you may be getting the same angle of view, when you use an APS-C sensor camera, each focal length's behavior changes compared to 35FF, because the capture format is differently-sized. Remember-the APS-C format brings the hyperfocal distance 1.6x closer than with 35FF, and remember that APS-C brings roughly 1.6x more DOF than 35FF at many focusing ranges with the same angular view as 35FF--BUT,and this is the big but, as the APS-C camera's focusing distance approaches hyperfocal focus distance, the depth of field goes up to 2.85x MORE DOF as compared with 35FF. Shorter focal lengths have closer and closer hyperfocal distances.
Lenses that capture equivalent angular field of view between APS-C and 35FF capture can be calculated easily, but the actual in-field and in-studio DOF and image "Look" performance between these two formats is HUGE,particularly in the wider-angle segment of many of the best professional lenses many people own, especially down in the 18-70 mm zone. But,alas, the inherently deep DOF that APS-C brings with it means that on APS-C, using a 100mm lens at distances that allow you to capture a half-body standing adult figure,the smaller capture format combined with the longer-than-expected camera to subject distance imposed by the cropped-off sensor means that an APS-C camera renders disturbingly in-focus backgrounds even at wide-ish apertures like f/4 with a 105mm telephoto. The small capture size of APS-C means that even f/4 yields pretty darn good depth of field--because you have to stand so FAR AWAY with a 100mm lens on APS-C! And,as those of us who've studied Depth of Field know, increasing camera-to-subject DISTANCE is the easiest way to achieving deeper,greater depth of field! And, APS-C pushes you back farther and farther from your subjects....bringing more DOF in the process. Or, APS-C forces you to use shorter and shorter focal lengths, thus also bringing more depth of field. This endless catch-22 is what drives longtime shooters like me to long for a digital 35FF camera option for Nikon F-mount lenses. I know what APS-C can do for me, and I like how it works most of the time. But there is a large difference between how APS-C and 35FF cameras actually render scenes; at the wide-angle focal length APS-C lacks wide-enough lenses to get as wide an angle of view as a 35FF can with a short lens,and also APS-C lacks lenses with sufficiently wide maximum apertures like f/1.8 to as wide as
f/0.7 or f/0.8 to give the dreamy 35FF out of focus background,limited DOF look at wide angles of view. At the widest end of the focal length ranges avaialable today, APS-C cameras deliver so much DOF that it becomes difficult,or impossible to get subject isolatation through shallow depth of field due to the deeper DOF the physically-smaller format brings with it.
Addendum: After I wrote this article, a very fine photographer named Robert Whiteman posted a nice studio portrait he has made, in defense of his personal desire to have a 35FF option for Nikon F-mount lenses. http://forums.dpreview.com/forums/read.asp?forum=1020&message=22519042
Whiteman's portrait shows the wrinkles on the muslin more-clearly than I would like; he writes, "However, with the cropped CCD I still have more DOF than I'd like to have for 3/4 and full length shots.FF would have had this background more out of focus with the same aperture... The background is 6+ feet away and I have no more room and shouldn't need it. With FF I am able to shoot a longer focal length with the same aperture and achieve the desired results with no problem. It's the easiest fix." end quoted passage from Robert Whiteman. His portrait shot was made at 38mm, f/5.6, on a crop-sensored Fuji S2 Pro.
So there you have it. An actual person,Robert Whiteman, posting one of his own studio portraits, and then calmly and reasonably pointing out what many would consider a flaw in his final results, namely that of too-deep background depth of field. Full frame and APS-C are actual,real,and different formats. The formats are actually different, with very different behaviors due to real,important differences in capture size,lens length,and angles of view,depth of field,and shooting distances.
Did you know that camera to subject distance and only camera to subject distance changes perspective? That's a true statement. Many people confuse perspective with the very real phenomenon of apparent perspective distortion that is often encountered when using a very short focal length lens. Also, close shooting distances in combination with short focal lengths brings with it what's known as foreshortening effects; you know, when the bride holds her hand forward toward your crop-sensored d-slr set to 18mm and her hand suddenly looks as big as an NFL defensive tackle's hand (but with a pretty manicure!) and her head looks like it's roughly the size of a grapefruit. Changing the format changes the camera-to-subject distances we typically are forced into shooting from, and the pictorial results,and the behavior of lenses change with the format's size, in many important ways. If one does not understand the science underlying capture format size and the relationship of focal length to the capture format's dimensions,then one needs to read some old-fashioned books on photography and optics. Most newcomers have never read a single page on lenswork or optics.
Many people do not understand why perspective is changed only by changing the distance from the lens to the subject. Many people speak of "wide-angle perspective" and "telephoto perspective", but many people are unaware that that there is no such thing as either "wide-angle perspective" or " telephoto perspective",and that those two terms are a gross mis-use of the term "perspective". And yet, on the web, there are those who don't even understand perspective and how it is regulated,and yet they insist in engaging in debate about the need,or usefulness even, of 35FF digital capture format d-slrs. These folks,who usually seem to know and understand only around half of the basic principles of lenswork as it relates to focal length and capture size,often state that they like how APS-C is working and they see no need for anything larger. Fair point,as far as it goes. If you do not know from experience what you've given up,or what you could be getting, then ignorance is indeed bliss. Hey,don't get me wrong--at times, the hugely-increased depth of field an APS-C sensor camera give you is a godsend,it really is. With shorter focal length lenses, it's possible to get very,very "deep" depth of field effects with relatively high magnification lenses and to be able to render big,deep swaths of the real world into good,sharp focus. If you want deep DOF, the smaller the format, the better.
"Equivalent angle of view" is not the same thing as "same kind of picture". The format of one's camera affects the way lenses of the identical focal length will perform;the same focal length of a lens will perform VERY differently on differing film or sensor "format" sizes.Ladies and gentlemen, APS-C is a different format than APS-H,which is 1.3x, and APS-C is a significantly different FORMAT than is Full Frame,aka 35FF, aka 24x36mm.
Take a look at what I've been blogging about...f/8, focus approaching hyperfocal distance, ie, focus set to about 20 feet, your cropped-sensor 20D's wide angle zoom lens is set to 31.25mm,and it makes a picture that has 53 feet of acceptable depth of field. Your 35FF camera,also capturing a diagonal picture angle of 46 degrees, has an 18-foot deep depth of field band. In this normal,real-world example, matching the angle of view of an APS-C sensored camera to that of a 35FF camera,the APS-C camera makes a picture that gives you a depth of Field band that's 53 feet deep, whereas Full Frame has an 18-foot deep zone of DOF. Who here cannot mentally "see" the difference in photographic result that the smaller capture format imposes,even though the angle of view is identical? Once again,let me reiterate, 35FF and cropped-sensor capture represent actual,different FORMATS.
Scaling down the format from 24x36 or 35mm Full Frame (aka 35FF) to APS-C makes the hyperfocal distance of a lens 1.6x closer than when the same lens is used on the 35FF format camera. When using cropped-sensored cameras, we often find ourselves moving FARTHER away from our subjects. And hey kids, guess what--nothing increases depth of field faster and better than moving FARTHER away from your subject! Wooo-hoo! The smaller-formatted camera forces you to move farther away,thus rapidly increasing depth of field. DOF is pretty shallow at close ranges, but as one moves the focus distance towards infinity,DOF builds rapidly and more rapidly,and then as one approaches the hyperfocal distance, DOF extends by leaps and bounds behind the focus point,stretching all the way out to infinity. The shorter the focal length lens one uses, the closer that lens achieves focus at its hyperfocal distance. And the smaller the capture size, the CLOSER the hyperfocal distance becomes! Making one's capture format smaller results in a complex shift in lens performance characteristics. Please, if you're not familiar with what I'm talking about, consult the article referenced here, and take note of the final two points Atkins makes:
4. If you use the same lens on an EOS 10D and a 35mm film body, then shoot from different distances so that the view is the same, the 10D image will have 1.6x MORE DOF then the film image.
5. Close to the hyperfocal distance, the EOS 10D has much MORE than 1.6x the DOF of a 35mm film camera. The hyperfocal distance of the EOS 10D is 1.6x less than that of a 35mm film camera.
Is it any wonder that I'm disturbed by how many overly IN-focus backgrounds I see these days with the proliferation of cropped-sensor cameras? I constantly see seamless paper rolls, muslin,and location backgrounds that are are competing for attention with the foreground subjects on many full-body or multiple-person photographs. Why are we seeing so,so many photos with very deep DOF these days? Because, as I've been writing about, the difference in depth of field between the very popular APS-C format camera and a 35FF format cameras, is HUGE, under a relatively large number of frequently-encountered,real-world shooting conditions. Typically,you're going to see from 1.6x more to 1.9x more to as much as 2.85x MORE depth of field with the same angular field of view coverage,at many "real-world" shooting distances when you shoot a cropped-sensor APS-C camera and not a 35FF format camera.
Perusal of the depth of field tables at http://photo.net/learn/optics/dofdigital/
will show that: 1)at close-range focusing distances the 1.6x Canons 10D-20D-30D will have 1.9x more DOF than 35FF. At "intermediate" focusing distances (which Atkins describes as 'not macro,not close to HFD'), the cropped-sensor Canon has 1.7x more depth of field relative to Full Frame. And as detailed above, at a focus distance close to the hyperfocal distance, the cropped-sensor Canons will show 2.85 times MORE depth of field,relative to Full Frame. Yes, the number is correct: 2.85 times more depth of field. That's almost three times more in-focus depth,in feet!
One really simple bit of proof that the difference between Full Frame and APS-C is actually a FORMAT difference manifests itself when you note that using an APS-C sensored camera brings each lens's hyperfocal distance roughly 1.6x times CLOSER than if using the same lens on a 35FF format camera. Yes,you read that right--using an APS-C camera shifts the hyperfocal distance of a lens 1.6x CLOSER than if one were using that same focal lenght lens on a 35FF format camera. Also,under real-world situations, APS-C brings with it from 1.9x more, to 1.6x more, to 1.7x more, to as much as 2.85 times MORE depth of field than what one would get if shooting on the entirely different full frame FORMAT capture size, while capturing the same angular view. The APS-C sensor brings with it a double-whammy if one wishes to limit or tone down background focus,especially at moderate distances or at shorter focal lengths. The smaller capture area "tends to pull everything into better focus." Take note,as focusing distances increase, APS-C picks up additional DOF at a truly astonishing rate; do not be persuaded otherwise by deliberately or innocently misleading examples of DOF on APS-C at close ranges like 6 feet...take a look at how much DOF APS-C renders at distances like 3 meters, 4 meters,5 meters, and so on.
Atkins has written an excellent article that attempts to illuminate and to cut through a lot of the total bullshit about depth of field that you'll hear and read on the web. His article allows those who do not understand the difference between cropped-sensor and 35FF capture to gain some real information on just how DIFFERENTLY lens focal lengths behave on different format cameras. What I am trying to show is that 35 Full Frame is actually a capture FORMAT. A format. In caps! Just like 120 rollfilm shooting 6x4.5 cm is a format. And 120 or 220 rollfilm shooting 6x6 is a format. And how the Pentax 6x7 represents a particular FORMAT. Just as 6x9 cm is a format. And 6x17 cm is a format. And how "4x5" is a format. There are real,actual,proven,well-known DIFFERENCES in the way cameras and lenses perform on different formats, but most newcomers have zero personal,real experience with anything other than APS-C and so they talk about stuff they don't understand from real experience,parroting a lot of internet myths,thus confusing the subject and muddying the waters for those striving to understand why "some people" want 35FF in digital slr bodies. The newbies often cannot seem to undertstand that moving to a teensy format can have REAL, and LARGE impacts on the pictures that can be made.
When one uses a small format camera like APS-C, lenses behave very differently than when shooting on a larger format camera. When switching from a full frame camera to a 1.5x crop or 1.6x crop camera, if all you compare is the "equivalent" angle of view you are going to be shocked when you make some images using the two different sized formats and look at the pictorial results. Just go to http://photo.net/learn/optics/dofdigital/ and scroll down and look at the three different colored DOF and focal length/format tables. Compare the 6x9 cm FORMAT with its 125mm lens and its 46 degree angle of view,and look at the total depth of field band depth in the three charts. Then look at the depth of field of 35mm and 10D when both are at 46 degree angle of view equivalence. Compare the 6x9 cm, the 10D, and the 24x36mm Full frame or "35mm" FORMATS,and you can see that depth of field varies *tremendously* between these three formats.
So many people have come into d-slr photography without experience in using say, a 120 rollfilm camera with a 75 or 80mm "normal lens" with its large negatives and rather shallow depth of field tendencies.I know a couple people who have some of the absolute BEST cameras and the absolute best lenses made, but who have never fired a single frame of 35mm film, but who nevertheless, have gone on to become very, very "into photography". I'm not trying to be elitist, but throughout photography's history, there has been a trend toward smaller and smaller film formats and many newcomers who argue that cropped-sensor cameras are "equal to" larger-sensored cameras really don't know what they are talking about. Smaller formats bring with them deeper depth of field tendencies. The actual "look" of images is format-dependent,and there's a different "look" to using a 150mm lens on 4x5 inch sheet film, and one hell of a different "look" to a 150mm lens on a DX-sensored Nikon. I know. I like the look of my Fujinon-W 150mm f/5.6 lens on 4x5 sheet film; on my 4x5, the 150mm
gives a nice,ever-so-slightly-wider than normal view. On a 1.5x d-slr, my 75-150 Series E zoom set to 150mm is quite a narrow-angle telephoto focal length. Let me say it again: 4x5,6x9 cm rollfilm,6x6, 6x4.5, 24 x 36mm, 125 square, 110,APS-C, APS-H,and 4/3 are all different formats. And the way lenses perform on these different formats is in no way "equal" or "equivalent" if all one does is try to get the same angle of view in a simple millimeter-for-millimeter equivalency of angle of view. Most newbies do the simple math and assume that equivalent angle of view equals "the same pictures",which is not true at all,not by a long shot. It's much more complicated than simply multiplying by 1.6x and "converting" focal lengths...the equivalence in angle of view does not square with the realities I've seen in 34 years of shooting pictures using formats as large as 4x5 inch to as tiny as 110.
I have owned a Bronica 120 rollfilm camera system for over 15 years,and I have a 65mm lens, an 80mm lens, and a 150mm lens for it. AND,and this is the kicker, it uses 6x6 and 645 backs,as well as 35mm film backs. I bought this multi-format Bronica system for its flexibility with 120 rollfilm. I have shot both 6x6 and 645 film thru the same body and lenses, and guess what--the cropped-down 645 format is actually noticeably different with the 65,80,and 150mm lenses than when shooting in the larger capture size of 120 square AKA 6x6. I've shot,and owned several 150mm lenses....and on different formats, 150mm behaves like a slightly-wider-than normal on 4x5, a nice medium tele on 6x6, a slightly-longer telephoto on 6x4.5, and on 35mm a 150mm is a slightly long medium telephoto, and on a cropped-sensored camera a 150mm lens gives a nice,tight angle of view. I think my experience on the Bronica system qualifies me to state unequivocally that a cropped-sensor d-slr is a camera that shoots in a different format than a 35FF camera. The difference is not simply in angle of view--the differences are much,much more fundamental. Cropped-sensored APS-C cameras capture their images in a different format than 35FF cameras do. We need to understand that different capture sizes have ALWAYS been considered to be different FORMATS. The rampant boosterism of the DX and APS-C crowd does not change the fact that the 35FF format is a different format,and has a different set of capbilities than other formats do. Those who tell you how to multiply focal lengths by 1.54x or 1.6x to get "equivalent pictures" with an APS-C camera really do not know what they are talking about in most cases;often, their arguments are simplistic,and based on something like having used ONE format for two years....they've often never shot anything larger than 35FF,and so they tend to be very partial to their pet format,and very sensitive to what they perceive as criticisms of the APS-C format's inherent tendency toward deep depth of field.
There's no need to be defensive about APS-C or "DX Format" as Nikon calls its 1.53x camera line....but there is a need to understand the truth behind different formats and how lenses of identical focal length perform VERY differently depending on how large the capture medium behind the lens actually is. The fact that Nikon,Pentax,Fuji,Sigma,and Olympus all make only cropped-sensored cameras has many users of those brands with their panties all in a bunch, constantly trying to tell experienced shooters that there's "no need" for a sensor larger than APS-C or 4/3. But,uh, Canon seems to have two cameras that capture to the 35FF format,and they are being used by many serious workers who really know,from their own actual experience, how making the capture format significantly smaller than 35FF significantly changes the way we can make pictures.
This one is for those who've never studied much about lenswork. Good page! A second,more primer-like http://www.cybercollege.com/m/mb_tvp012.htm
I discovered this article after I wrote the main blog entry;this article from 2003 covers the myth of the "crop factor",and explains,lo and behold, that cropped-sensored d-slr's represent a different format of camera than 35mm full frame! Australian landscape photographer Nick Rains wrote a very,very,very good article explaining how thre is no such thing as a "magnification factor". His article is an absolute must-read for those looking to sort the bullshit from the facts.
This on-line calculator has the BEST illustrations of ANY on-line DOF calculator. Great little drawings are rendered with each computation. Kudos!
http://www.earthboundlight.com/phototips/perspective-subject-distance-focal-length.html An article entitled Working With Perspective,Subject Distance and Focal Length. A nice short article,with some nice illustrations.
Focal Length of a Camera Lens,http://hypertextbook.com/facts/2002/MiriamJanove.shtml
http://photo.net/equipment/medium-format/focal-length-conversion in an article entitled Equivalent Lens Focal Lengths For Different Film Sizes. This article deals with how different focal lengths are rendered differently, based on the capture format's physical size. This is the part of the science where many people are weak.
A page entitled simply Rui Salgueiro's field-of-view calculator,this allows you to input different values for many different FORMATS of cameras,such as 24x36mm (aka 35mm film, aka 35FF), 14x36mm (aka 135- or 35mm panorama), 6x6 (56x56mm), 645 (41.5x56mm), 6x7cm (55x70mm), APS-H (16.7x30.2mm), APS-C (16.7x25.0 mm), APS-P (10.0x30.2mm), 4x5 inch (101.6x127mm), 5x7 inch (127x177.8mm), or 8x10 inch (203.2x254mm). Plus, a custom-configurable field with user-selected width and length parameters.