# The fallacy of 35mm "equivalent focal lengths"

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Re: The fallacy of equating "focal length" with "reach"
6

Tony Beach wrote:

Gerry Winterbourne wrote:

Tony Beach wrote:

Preface

Ironically, even here at DPR equivalent focal lengths are often divorced from a complete understanding of what is or isn't equivalent. There is this idea that if a lens covers a certain FOV on a given format then it is somehow equivalent to whatever focal length that would cover that FOV on a 35mm format camera.

Focal length as such is simply a dimension. The width of field of view is simply a dimension. Those two dimensions can be related by simple geometry. If we also know the width of the sensor (which determines the width of the field of view) we can understand what focal length we need to get our picture to fit that width.

That knowledge can be just abstract; but in communicating it to others we need a datum. By common consent that datum is accepted as using the old 35mm frame size. From the point of view of relating focal length to field of view "equivalent" is a correct and sensible usage.

Coming from DX format I have never considered this a sensible approach. My lenses didn't suddenly grow or shrink because I used them on a different format.

And no one has said or suggested otherwise. But I used DSLRs for 30 years before moving to (crop) DSLRs. I had to learn that if I wanted the field of view I was used to at 50mm I had to use 35mm instead (which actually gives the FOV of 52mm, but that is near enough).

So in terms of field of view only, the 35mm equivalence exactly fits my needs - and, by extension because it's widely used - those of many other photographers.

When you bring "reach" into consideration there are other things than just field of view to take into account - lens resolution, pixel resolution, depth of field etc. However, they have nothing to do with the equivalence of field of view. Everything you say below may be true (I've read it but not scrutinised every detail): but it simply doesn't apply to your headline thread title.

By all means discuss reach if you want; but don't confuse people by equating it with focal length and/or field of view.

What if I told you that my NIKKOR 28-70mm lens is a equivalent to a heavier 80-200mm lens? Would you find that information useful

No, because it isn't true. Untruths are never helpful; and introducing irrelevant untruths into a discussion is either deceitful or silly (or both).

If you said something different - that the field of view from the first lens on a crop camera would give the same fields of view as a 42-105mm lens on a 35mm camera; and if coming from 35mm I wanted to approximate a 42-105mm lens (even though I'm not aware that one has ever existed) I would find that information useful.

considering that I can easily accomplish that better with that lens than what can be done with my S95?

Again, utterly irrelevant. Mention (which you haven't) the focal length range of the S95 and it might be peripherally interesting but as I happen to know that it corresponds to neither 80-200 or 42-105 it can't be at all helpful.

After some testing with various lenses I concluded that at 35mm my NIKKOR 28-70/2.8D matches the longest focal length of my S95, so it's a third of the published 105mm "equivalent" focal length of that compact camera.

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Definition of "reach", and an example/comparison
1

Is your essential point here that, depending on optics, pixel density and output size, you may get better results for a particular field of view from a crop on one camera using a shorter equivalent focal length than from the full frame on another camera using a longer equivalent focal length? And where that was the case the "reach" of the shorter equivalent focal length would be greater than the reach of the longer equivalent focal length? Hence your point that there is more to reach than equivalent focal length?

So, for example, the full frame from a ZS70 at 129mm (720mm equivalent focal length) might not be as good as a crop from a D800 with a 28-70 at 70mm (70mm equivalent focal length).

I just did an experiment along somewhat similar lines. I captured an image using 720mmm equivalent with a TZ90 (ZS70). I then captured the same scene, focused on the same area (the notice board) with an A7ii with 24-240 at 70mm. I then cropped the A7ii image to match the TZ90 full frame. Here is the extent of the crop. It measured 609 x 456 pixels.

I did the same at 105mm on the A7ii, with this crop, which was 901 x 676 pixels.

I then output all three at 1080 pixels high.

TZ90, full frame

A7ii, cropped from 70mm

A7ii, cropped from 105mm

For these particular cameras, focal lengths, pixel densities and output size it seems to me that the TZ90 has greater reach than the A7ii with 24-240 at 70mm and 105mm focal length.

Postscript.

With the 24-240 at 240 it was closer, but I think the TZ90 was still a little better.

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Re: The fallacy of 35mm "equivalent focal lengths"
5

Tony Beach wrote:

TonyGamble wrote:

Then apparently you stopped reading after the first paragraph.

I did Tony.

I should have put the second paragraph in front of the first one.

Have you got time to write a precis if what you are saying is important to us DPR folk.

Describing a lens as having an equivalent focal length is simply wrong. I can't make it any more concise than that.

The longer answer is that a lens has its own focal length and no other, and that has a direct bearing on how large its aperture is which in turn determines how much light comes through it, and when the aperture becomes very small it imposes diffraction (see the upper right corner crop).

I think the problem is that you have not understood the concept of "equivalent focal length" or want to include more things not included in it. It is only a concept that describe FOV of lenses on different sensor formats, nothing more, nothing less.

"equivalent focal length" is a standardised specification on cameras that is controlled by CIPA, just like many other specifications.

It does not say anything of the performance.

In my testing this week I found that I can take a 45mm or 50mm lens used on my D800 and use it to more effectively capture the "equivalent" of a 105mm lens than a camera (my S95) that a few years ago was advertised to go to 105mm "equivalent focal length." Thus, when I see that the camera I'm going to replace it with is being marketed both here at DPR and everywhere else to be a 720mm "equivalent" I thought it would be useful to some to point out why that's a fallacy and my expectation is that its reach will be closer to 350mm (for my D800 -- the number changes depending on the camera, so with some of the newer models it might be more like 300mm and with many of the lower pixel density cameras it might be more like 400mm; and of course there is the issue of which 300-400mm lens you are using).

It looks like you want to get equivalence of a lot more factors than FOV.

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Re: The fallacy of 35mm "equivalent focal lengths"
1

Tony Beach wrote:

jrtrent wrote:

Tony Beach wrote:

jrtrent wrote:

Tony Beach wrote:

Preface

Ironically, even here at DPR equivalent focal lengths are often divorced from a complete understanding of what is or isn't equivalent. There is this idea that if a lens covers a certain FOV on a given format then it is somehow equivalent to whatever focal length that would cover that FOV on a 35mm format camera.

And I thank them for divorcing other issues from this basic and useful concept.

Then apparently you stopped reading after the first paragraph.

Then you read the part where I wrote that, " 'Reach' is one of the factors I was considering, " in deciding which camera to buy for my girlfriend's birthday.

I just disagree with you that optical resolution, pixel density, and aperture diameter have anything to do with equivalent focal length.

It's more fundamental than that. There is no such thing as an equivalent focal length, there is just a focal length.

I currently use two different digital cameras, a crop sensor DSLR and a smaller-sensored compact, but whichever one I shoot, I choose a focal length for its field of view, and 99% of the time my chosen focal length is about a 50mm equivalent.

Again, the only thing that is equivalent is the FOV.

Field of view is the primary thing I consider when I buy a lens or set a focal length on a zoom lens, and the concept of there being equivalent focal lengths for the lenses I grew accustomed to with 35mm film has been helpful. The viewfinder in my compact camera actually displays focal length in 35mm equivalent terms, making it quick and easy for me.

Over the years, I've moved to using a 50-55mm equivalent focal length almost exclusively, but back when I carried 35, 50, and 85mm lenses for my 35mm SLR, each focal length gave a unique look to the image, so each had its use and purpose. In your original post, you gave examples of cropped images, and if you're willing to crop and do your composing in post-processing rather than in the viewfinder, then maybe focal length and its accompanying field of view isn't very important to you, but it's of primary importance to me.

I've come to use a standard focal length lens because I prefer the way it renders a scene compared to either wide angle or telephoto lenses. There used to be an article here at DPReview by Andy Westlake that described the quality it gives to a picture:

"A telephoto lens, for example, renders distant objects larger in the frame, and has the effect of compressing the apparent spatial relationship between objects. A wideangle does precisely the opposite; in squeezing more content into the image, objects appear smaller and more distant. It's in the happy medium between these two extremes that the standard lens lies; the apparent sizes and spatial relationships between image elements appear natural, and much as they did in real life."

If I crop an image made with a 50mm equivalent lens, then it loses that normal field of view, and the scene no longer looks as natural and realistic as it did before, so I don't crop.

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Re: The fallacy of 35mm "equivalent focal lengths"
5

Donald B wrote:

nothing wrong with good quality small cameras, oly xz1 and canon 5dmk2 at the same venue these are heavy crops and af used on both cameras.

Don

Both are pretty bad (I know you are a good photographer; you had dreadful lighting here). Did you take both?

The Canon shot is just awful - completely out of focus. In focus it would likely have been the better of the two. That model of Canon can definitely do a lot better than that in poor lighting.

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Re: The fallacy of 35mm "equivalent focal lengths"

New Day Rising wrote:

Donald B wrote:

nothing wrong with good quality small cameras, oly xz1 and canon 5dmk2 at the same venue these are heavy crops and af used on both cameras.

Don

Both are pretty bad (I know you are a good photographer; you had dreadful lighting here). Did you take both?

The Canon shot is just awful - completely out of focus. In focus it would likely have been the better of the two. That model of Canon can definitely do a lot better than that in poor lighting.

I was asked to shoot this image with a 5dmk 2 I was covering the event with my k7 with a studio setup and the main photographer asked me to use her camera, I was interested in a comparison so I ran down stairs and got my xz1 for a quick test shot. the lighting was stage lighting only their was about 200 students on the stage and as I said this is like a %500 crop I processed all the images for the night and my k7 blew the canon away for the studio work and my little xz1 did the same the af on the canon was pathetic and this was the best shot I took with it. its why ive never bought a ff they just don't work for me and what I shoot. GB loves this image

Don

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Needs definitions
2

Hi Tony, skimmed through it twice but got hopelessly confused.
I'd recommend re-writing it to make more concise and also to add in the definitions of the various terms you're using.

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Re: Needs definitions
2

hesbehindyou wrote:

Hi Tony, skimmed through it twice but got hopelessly confused.
I'd recommend re-writing it to make more concise and also to add in the definitions of the various terms you're using.

Hi again,

I read through the replies and it looks like you think that it would be less confusing if equivalent focal length stopped being used to refer to a field of view that's equivalent to full frame camera, and instead changing its meaning to refer to something like:

'the equivalent image quality taking into account the sensor too'.
I think that would confuse everyone

Another poster wanted to do a similar thing with redefining aperture as he objected to an f1.8 lens on a smaller sensor giving a different image quality & depth of field to an f1.8 lens on a larger sensor.

Essentially, we've got a fairly simple and limited concept that tells part of the story and some people want to divorce that figure and definition from its current, limited, logical meaning and confuse it into a single number that defines what, for want of a better word, I'll call 'image quality'.

It's not possible as things like focal length compression and exposure mean there is no equivalence-in-all-respects for you to attach a single number to. Attaching a number to what things you can (or think you can) leaves you back where we are now (with multiple factors to take into account) but with a system that's arbitrary, difficult to measure and impossible to be objective about.
Best we accept the limitations of what is meant by equivalence and be aware of what it doesn't take into account.

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My opinions
10

I am going to state some of my opinions but this is a complex area and others may disagree or I may make some errors.  Please feel free to disagree or correct errors.

As others have said, the usage of "equivalent focal length" on this site and elsewhere is well defined and useful.  The concept of "reach" put forward by the OP is not well defined and its usefulness, to me at least, is limited.

"Equivalent focal length" is useful for questions like:

• What is the best focal length for head and shoulders portraits?
• What focal length do I need to photograph the interior of Notre Dame in Paris?
• What focal length do I need to photograph soccer games from the sideline?
• What focal length do I need for a safari in East Africa/South Africa/India?

"Reach" is not useful for the first three questions and only of limited use for the fourth because other variables such as light, terrain and atmospheric haze affect the answer.

I think that "reach", as used on this thread, seems to be based on extreme situations where you need to go to 1:1 resolution to see the target.  Birders have a rule of thumb that in these situations you need to use the camera that gets the most "pixels on the target". So birders would be familiar the idea of "reach".  The OP's example (in one of his later posts) of trying to photograph a coyote on a hill would also be subject to this rule.

However, very few of us use 100% crops in, for example, competitions.  Why?  Because, if you need a 100% crop, then image quality is going to be poor anyway.  So we switch to a longer lens or get closer if we can.  In my case, if I can't do either of those, I don't take the shot.  The OP's coyote on a hill some distance away would be an example of this, especially if it was moving.  I would take a shot and blow it up if I needed to confirm that it was a coyote, but I wouldn't expect that shot to be usable for anything else other than that.

So, for me "equivalent focal length" as used on this forum is a very useful concept.  The OP's concept of "reach", if it could be defined and measured, might also be useful for some situations, but it wouldn't replace "equivalent focal length".

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Re: The fallacy of 35mm "equivalent focal lengths"

Tony Beach wrote:

Preface

Ironically, even here at DPR equivalent focal lengths are often divorced from a complete understanding of what is or isn't equivalent. There is this idea that if a lens covers a certain FOV on a given format then it is somehow equivalent to whatever focal length that would cover that FOV on a 35mm format camera.

[This is a good place to suggest to anyone that doesn't want to read a long post (I usually don't like reading long posts) that you might want to skip to the picture below and take a long look at it and draw your own conclusions. Just be prepared for me alluding back to the "Getting into the weeds" portion of this post if you have any questions or concerns about what I'm presenting.]

The reason for this post is that I got to thinking about "reach" the other day as I was researching a compact camera to give my girlfriend for her upcoming birthday. “Reach” is one of the factors I was considering, and I’ve settled on a Panasonic Lumix DC-ZS70 with (among other features I think will be valuable to have) its 20 MP sensor and a 30x zoom. However, I don’t for a minute buy into the “24-720 mm equivalent focal length” which is how the camera is marketed (for instance, here and here). Will this new camera get more reach than the Canon PowerShot S95 it will be replacing? Undoubtedly, but I will have more to say about that later this week when I have the new camera in hand. Will it get more reach than I have with my D800, NIKKOR 70-200/2.8 VR and TC-14eII? I'm thinking it should, but that too remains to be seen.

Getting into the weeds

There are three things that add up to reach:

1.) Optics -- which includes the actual focal length (and not the equivalent focal length), and just how good the optics are (I looked at a 70-300mm lens for my D800 and it was sent back because it didn't have any more resolution at 300mm than the 200mm lens focal length I already had).

2.) Pixel density -- which is essentially how many linear pixels in a mm of the image circle covered.

3.) Aperture diameter -- which is what true equivalence is all about. As it relates to reach small apertures have more diffraction, and because smaller apertures restrict light coming to the sensor the exposure ends up being noisier which in turn negatively effects resolution.

Given all of that, what is the actual “equivalent” focal length of the Canon PowerShot S95 compared to what I routinely get with my D800? After some testing with various lenses I concluded that at 35mm my NIKKOR 28-70/2.8D matches the longest focal length of my S95, so it's a third of the published 105mm "equivalent" focal length of that compact camera. I expect the DC-ZS70 to do better than the S95 with its 129mm lens rather than the 22.5mm lens on the S95, and with its 840 pixels per linear millimeter rather than the 490 pixels per linear millimeter on the S95.

Will the DC-ZS70 do better than what I get from my D800 with my longest current focal length? Well here's the math so far for the D800 compared to the S95:

At 35mm my D800 with its 204 pixels per linear millimeter beats my S95 at 22.5mm with its 490 pixels per linear millimeter. That's not true of all the lenses I tested, and some could possibly do even better, but I did test my old NIKKOR 18-70 DX kit lens and at 50mm it barely matched the S95. One might have expected the S95 having 2.4x as much linear resolution as my D800 at the sensor level would translate to its 22.5mm lens being equivalent to a 54mm lens, and while reasonably close to that it's only 65% of the way there (35mm rather than 54mm). Some of this is about optics, for sure; but as I will show in the visual examples below diffraction is also a factor.

Maybe I should break out my D300 and crop its final output to 4:3 aspect ratio, which would work out to 10.8 MP and be a bit closer to the 9.98 MP for the S95, but at 181 pixels per linear millimeter that's only a difference in linear resolution per millimeter of 12.5% more for the D800 (i.e., it's barely noticeable). The thing is when it comes to focal length equivalence (if you define that as reach rather than FOV coverage area) is that it's not about the sensor's format or aspect ratio, it's about the relative pixel densities -- so if I put one of my 105mm focal length lenses on my D300 you're going to have a hard time at the pixel level telling the difference between its output on that camera and its output on my D800 (the one thing that will be obviously different will be the FOV, but that's not reach).

Given all of that, I'm expecting the reach of the ZS70 at about 105mm to beat my current longest lens on my D800. I'll try to test that hypothesis next week. In the meantime...

A picture is worth a 1000 words (if not more)

Okay, so now comes the visual evidence to back up what I'm writing about here:

As always, it's important to view this at its "original size" or "100% zoom."

My final thoughts (for this post)

For me that upper right crop at f/22 says a lot. Why? Because the aperture diameter at f/22 for a 90mm lens is 4.09mm, and that's (essentially) the same aperture diameter as f/5.6 for the 22.5mm lens used on the S95 (4.02mm). The middle crops are basically "web size," which in this context is the full frame of the S95 file and the equivalent FOV of the D800 file both sized to 1080 vertical pixels in height -- and for all practical purposes that's enough for a lot of people, and if that's the case I could probably have taken a good 20mm lens and gotten "good enough" results on my D800 under these conditions.

Well written. In a big overview I think "equivalence" created more confusion than it was worth. Taking the sensor and "mechanics" out of the equation, it's more about magnifications, and angles of view, the optics. What does 20X mean in common terms? Why equivalence in 35mm terms? It's such an old point of reference. (Been there.)

I use MFT. I don't think "2X (or 1/2) equals 35mm, so...". 14mm is wider, 150mm is narrower, 20mm is close to the human eye, etc. I'd lose my train of thought if I had to calculate every sensor size.

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Re: The fallacy of 35mm "equivalent focal lengths"
6

Donald B wrote:

New Day Rising wrote:

Donald B wrote:

nothing wrong with good quality small cameras, oly xz1 and canon 5dmk2 at the same venue these are heavy crops and af used on both cameras.

Don

Both are pretty bad (I know you are a good photographer; you had dreadful lighting here). Did you take both?

The Canon shot is just awful - completely out of focus. In focus it would likely have been the better of the two. That model of Canon can definitely do a lot better than that in poor lighting.

I was asked to shoot this image with a 5dmk 2 I was covering the event with my k7 with a studio setup and the main photographer asked me to use her camera, I was interested in a comparison so I ran down stairs and got my xz1 for a quick test shot. the lighting was stage lighting only their was about 200 students on the stage and as I said this is like a %500 crop I processed all the images for the night and my k7 blew the canon away for the studio work and my little xz1 did the same the af on the canon was pathetic and this was the best shot I took with it. its why ive never bought a ff they just don't work for me and what I shoot. GB loves this image

Don

It was probably because you hadn't used the 5D before - there is no way it could have been such a successful camera if the autofocus really was that bad

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Re: The fallacy of 35mm "equivalent focal lengths"
1

thinkinginimages wrote:

I think "equivalence" created more confusion than it was worth.

I've often wondered why we don't just go with field of view? I'm assuming that it's because it's not a property that's inherent to the lens but will also involve the sensor... imagine how confusing that'd get between 35mm, Canon APS-C, everyone elses' APS-C

What does 20X mean in common terms?

On a camera, 20x zoom means it goes to 20 x the minimum focal length

Why equivalence in 35mm terms? It's such an old point of reference. (Been there.)

Because it was a common frame of reference for those coming from 35mm.

I use MFT. I don't think "2X (or 1/2) equals 35mm, so...

Given that it's essentially just a way of comparing angle of view between different systems, I wouldn't expect anyone does the calculations when using their own system - it's not for that.

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Re: The fallacy of 35mm "equivalent focal lengths"

hesbehindyou wrote:

thinkinginimages wrote:

I think "equivalence" created more confusion than it was worth.

I've often wondered why we don't just go with field of view? I'm assuming that it's because it's not a property that's inherent to the lens but will also involve the sensor...

It's not just that although it is, of course, a factor. What do we mean by field of view? If we mean width there's the problem that it gets wider the further away the scene; so the FOV for portraits at a few metres away would be tiny compared to the FOV with the same lens used for a landscape. So we'd really have to mean angle of view.

But I've never come across anyone who thinks of scenes in terms of how many degrees (or radians) they cover. And angle of view isn't linear with focal length - especially at wide angles - so there's another complication to have to deal with.

There have always been different formats, going up to full plate. While it's silly to contemplate putting a full plate lens on a 35mm SLR there has always been some ability to swap lenses between formats. Now, it's easy to print the focal length of a lens on a body and it is a single number regardless of the body used. But printing the angle of view is tricky because you'd have to do it for every format the lens might be used on, as you say ...

imagine how confusing that'd get between 35mm, Canon APS-C, everyone elses' APS-C

What does 20X mean in common terms?

On a camera, 20x zoom means it goes to 20 x the minimum focal length

Why equivalence in 35mm terms? It's such an old point of reference. (Been there.)

Because it was a common frame of reference for those coming from 35mm.

I use MFT. I don't think "2X (or 1/2) equals 35mm, so...

Given that it's essentially just a way of comparing angle of view between different systems, I wouldn't expect anyone does the calculations when using their own system - it's not for that.

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Equivalence does not
15

Camera equivalence theory does not take into consideration any of these factors:

• Megapixels
• Lens aberrations
• Camera processing or post-processing for the most part
• Bokeh (the quality of blur)
• Dynamic range
• Image aspect ratio
• Sensor technology and quantum efficiency
• Angle of view of lenses that aren't rectilinear
• Lens transmissivity (T-stops vs f/stops)
• Film vs. digital
• Lens microcontrast and modulation transfer functions (MTF)
• Changing camera positions or perspective changes
• Color, contrast, saturation, or sharpness
• Ergonomics

Equivalence only describes how photography changes with scale or size. It is pure geometry with a little physics and nothing else. It is simply an application of the geometric Law of Similar Triangles, or what is called isometry in the sciences. Equivalence is the stuff that's pretty much always guaranteed to be true, at least approximately, without regard to specific technologies or brands or times or practices, and it describes 19th century photography as well as 21st century photography, DSLRs, Mirrorless, large format, smartphones, etc., without bias.

Of course you can put any of the above factors into an equivalence analysis (and sometimes you have to) but then the theory becomes very specific and no longer generally applicable, and you risk "losing the forest for the trees", getting lost in specific minutiae.

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Re: Equivalence does not

My apologies if this was brought up, some of this is over my head.

At f/22, defraction is going to be an issue anyway, so heavy crops are generally out of the question. It’s difficult to compare IQ with f/5.6 and f/22. Most start at around f/13, give or take. I can get stupid good crops at f/8-f/13, and anything above that starts to deteriorate a bit. At f/22, my crop goes from being decent at even 125% to similar quality at 50%.

I am bringing this up because I wondered if it was even conclusive to have anything at over f/13.

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Re: The fallacy of 35mm "equivalent focal lengths"

I agree. My point was more from the perspective of someone entering photography or not interested in the math.

For us, I think it's time to move away from the film reference. It's a bit tedious and eventually it's going to "age out". "Full frame" is going to be equally obtuse because you'd need to know what that means.

Maybe a better "constant" is the human eye. Let's consider it a factor of 1. Surprising enough, that's been measured at about 43mm and a 55 degree angle of view.

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User errors, not the camera
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Donald B wrote:

nothing wrong with good quality small cameras, oly xz1 and canon 5dmk2 at the same venue these are heavy crops and af used on both cameras.

Don

Another false comparison from you , Donald. The Canon shot would be much better if you used the same 1/60 shutter speed and -1/3 EC, and had focused properly. You admit below that you didn't know how to use the Canon. Why imply this shows a comparison of camera body capabilities if one of the images images hasn't been taken properly?

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So two lenses of same focal length on same camera aren't equivalent
7

The logical extension of what you are saying is that the 28-70mm 28.D @ 70mm on your D800 isn't equivalent to the 24-70mm 2.8E @ 70mm on the same camera because the latter out-resolves the former.

I have to wonder how useful a definition of focal length equivalence that is.

That is not to say that it isn't useful to know that one lens / sensor combination will out-resolve another,

But let's go further. You also take into account the effects of the sensor in your assessment of "equivalence". So by your approach, the 24-70mm 2.8E @ 70mm on a D5 at 1/125 f/4 ISO 100 isn't equivalent to the same lens on a D850 at the same settings.

When a lens isn't equivalent to itself when used at the same settings, I think we've gone too far off into the weeds.

Focal length equivalence of a lens is a property of the lens, not of a lens/body combination. The very real effect you are describing does not negate the concept of focal length equivalence. Rather it points out that one shouldn't expect same quality outputs from equivalent focal length, even at identical pixel counts.

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Re: The fallacy of 35mm "equivalent focal lengths"
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thinkinginimages wrote:

For us, I think it's time to move away from the film reference. It's a bit tedious and eventually it's going to "age out". "Full frame" is going to be equally obtuse because you'd need to know what that means.

So you'd swap one fairly arbitrary frame of reference...

Maybe a better "constant" is the human eye. Let's consider it a factor of 1. Surprising enough, that's been measured at about 43mm and a 55 degree angle of view.

...for another frame of reference that's inexact and open to varying degrees of interpretation.
I reckon we stick with what we've got - actual focal length within the system and then a convention that allows us to compare angle of view between systems.

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Re: The fallacy of 35mm "equivalent focal lengths"

I don't know how to put this gently, but you might want to reconsider how you have written this.

Tony Beach wrote:

Ironically, even here at DPR equivalent focal lengths are often divorced from a complete understanding of what is or isn't equivalent.

The DPR people have written quite clearly and correctly about this.  They really do understand it.  You might want to review here what it covers and what it doesn't.

There is this idea that if a lens covers a certain FOV on a given format then it is somehow equivalent to whatever focal length that would cover that FOV on a 35mm format camera.

By definition it is somehow equivalent.

The fallacy of 35mm "equivalent focal lengths"

It's good that you're working through this for yourself, but it's probably not a good idea to claim that you have found a fallacy.  That explains the negative reactions you have gotten.  I think you are probably confused about what equivalence covers.

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