Full frame equivalences for lenses

There is no formula for what each individual sees and how each individual interprets visual data.

Morris
I think the confusion is you are using the word equivalence in the english meaning of "the same" whereas everyone is using the photographic definition of the word equivalence, which has a set definition.

You may object to the fact that photographers of yore have chosen to use the english word "equivalence" for their narrow technical definition they call equivalance, but that is the way people are using it.
When people use the direct terms such as Field of View, there is agreement. The rest of equivalence as used by photographers leads to arguments, mis understandings and more just as we have here.

Morris
These are my thoughts Morris, it’s great for field of view comparisons, the rest is largely just posturing.

The actual difference in depth of field is fairly minuscule anyway, as is the out of focus properties. Yes you can make the differences more exaggerated with careful composition but largely that one stop doesn’t mean much.



same with noise, it’s only relevant at the extremes, when you actually start looking around, barely anyone is hitting those extremes. So in the end it just becomes a battle of the spreadsheets, who can put all the numbers to their advantage.



The absolute worst of it all is when you see people use it to try to tell others that they can’t use certain cameras to do certain jobs (Fuji for wildlife etc) and 99% of the time it’s just nonsense.
 
It seems to me people want to rubbish the exposure triangle for nothing more than reasons of petty snobbery, to simply start an argument, or to somehow come across sas having some kind of superior knowledge, and honestly I have no idea why.
This was a thread that was answered correctly in one word in the first reply.

If everyone had left it at that, none of this would have been needed 🙂

The only reason it’s descended into this familiar exchange is that people started saying that the correct answer wasn’t. Inevitably, that invites a reasoned explanation as to why it is the correct answer. The thing is that the “exposure triangle” is a contributor to the confusion around equivalence, so as much as it is indeed a helpful thing if you want to shoot JPEGs or even convert raws to JPEGs with relatively little fuss, when it comes to explaining equivalence it very much gets in the way.
 
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There is a lot of agreement between the video and what Richard states yet the example of DOF and exposure with the same lens and what happens when you crop is what people here don't seem to get.
If you crop an APS-C region out of any sized sensor, you have effectively used an APS-C camera, so you get the same results. That's not what was being discussed.

The OP asked if his 16-55mm F2.8 lens is equivalent to a 24-80mm F4 lens used on full frame. The answer is yes.

Let's narrow it down to just the 24mm setting on the APS-C camera, to keep things simple.

If you take a photo at 24mm on the APS-C camera and at 24mm on a full-frame camera from the same position, they will be radically different photos: you've either framed badly on the full-frame one and included lots of extra stuff that you need to crop away, or you've cut the edges off the scene on the APS-C shot.

They're simply not the same photo. One is presumably the photo you want, the other isn't.

If you crop in to the APS-C region of the full-frame camera, then you've effectively used an APS-C camera and should probably think hard about your composition or lens choice.

Which is the point.

If I stand in the same position (because there are plenty of instances where you can't move freely to whatever location you want), and want to take a photo with the same framing as the 24mm on APS-C, you'd need to zoom to around 36mm on the full-frame camera.

That accounts for what the OP was saying in terms of the focal lengths being equivalent and that's why we're not comparing 24mm on both systems: because they'd take different photos.

And that's all video says too: if you use a different sensor size, you'll end up using different lenses (potentially with different aperture diameters), and it's the different lens, not the different sensor size that makes the difference.

Obviously it's the combination of sensor size and appropriate lens that has the impact we're discussing (hence the comparison between the 16-55mm lens and a hypothetical different lens with different focal lengths on a different system).

It's wrong to say it's caused by sensor size alone, but it's equally peculiar to say it's only caused by focal length alone because, while it's strictly true, it presupposes that you're picking a focal length with no consideration of what sensor you're mounting it on, which is just not how any photographer I've ever met thinks.

Richard - DPReview.com
In addition, I would point out that d'Entremont uses the same lens and f-stop with both cameras to make the photos. That means both photos are made with the same lens entrance pupul diameter.

This is a central tenet of equivalence: equivalent photos are made with the same entrance pupil diameter. This ensures both photos have the same depth of field, are made with the same total light, and have the same noise. As Richard explained, cropping the full frame image to match the framing of the APS-C image simply completes the process.

That section of d'Entremont's video essentially demonstrates the effectiveness of equivalency as a tool for determining which settings allow different format cameras to make the same photo.
 
It seems to me people want to rubbish the exposure triangle for nothing more than reasons of petty snobbery, to simply start an argument, or to somehow come across sas having some kind of superior knowledge, and honestly I have no idea why.
This was a thread that was answered correctly in one word in the first reply.

If everyone had left it at that, none of this would have been needed 🙂

The only reason it’s descended into this familiar exchange is that people started saying that the correct answer wasn’t. Inevitably, that invites a reasoned explanation as to why it is the correct answer. The thing is that the “exposure triangle” is a contributor to the confusion around equivalence, so as much as it is indeed a helpful thing if you want to shoot JPEGs or even convert raws to JPEGs with relatively little fuss, but when it comes to explaining equivalence it very much gets in the way.
My problem is the overall dismissal of it as a useful tool, rather than anything to do with equivalence. I understand that’s a bit off topic in this particular thread but it just annoys me when I see it being dismissed. I personally found it a really good common sense visual aide for what each setting means at its most basic level, and it allowed me (via a Brian Peterson book) to dive straight in with using manual on my first camera.

It’s been stigmatised and I can’t help but think that sometimes it’s nothing more than people sneering at it a little. Having some massively scientific explanation as to why it’s not accurate or why ISO isn’t part of the exposure is just completely missing the point of what it’s there for.
 
Yeah I did have the smiley. But internet rules dictate that holy wars must be fought in full every time.
 
Assuming equal sensor technology
Who has equal sensor technology to Fujifilm?

with a different color filter array.
Thanks, so not the same then.
Basically the same. The underlying hardware is definitely the same. With the medium format sensors, those use a standard Bayer color filter array and are the same Sony sensor used in other medium format cameras.
But not the same, so there are variables that can and will impact how the final image is displayed. Much in the same way a Canon sensor will differ from a Sony one, or a bespoke Nikon sensor will differ from the other two. Given how important the processor is in the process of producing the final image, that also plays a part in this too.

So your assumption about sensor technology is completely wrong, im sorry.

The camera companies cant even operate using the same ISO standards.
Are there sensor technology differences that impact quality? Yes. In the context of modern sensor produced in the last few year, are the differences meaningful? No. The image quality differences between any APS-C sensor and any full frame sensor are far greater than the difference between a Canon APS-C sensor and a Fuji APS-C sensor.

The one exception to this would be the Sony A9 III with its new global shutter sensor, but that is a sensor with significantly different technology.
So the image quality difference between a 15yr old Full frame camera and a 2025 APS-C camera will be great will it?
How are those two "equal sensor technology"?
You said ‘“the image quality difference between ANY APS-C sensor and ANY full frame sensor are far greater”

You seem to be not very good at reading, or choosing not to, one of the two.
You are just arguing for the sake of argument. My exchange with you started with "equal sensor technology"
 
Rather than quoting walls of text, ill pose some basic questions around the exposure triangle.

Can someone tell me, as a beginner, what is wrong with using this as a way of showing the relationship between the 3 main functions of a camera, and using it as a tool to learn how my camera works.

6b97299be4a2423db42bccb7e36263c4.jpg

It seems to me people want to rubbish the exposure triangle for nothing more than reasons of petty snobbery, to simply start an argument, or to somehow come across sas having some kind of superior knowledge, and honestly I have no idea why. It's a simple drawing/table that lets people understand the physical relationship between the 3 settings, and how changing one of them impacts the final image.

Set ISO to 0 and you get no exposure, increase it in line with the other 2 settings and you get an exposure. Removing it from the learning process offers nothing and claiming this 'triangle' of exposure is incorrect offers nothing.

It's a bit gatekeepery at the very least.
Equivalence is not "gatekeepery" and it is not in conflict with the exposure triangle. They are two very different concepts. I think most of the confusion in this discussion comes from people who think the exposure triangle equals equivalence.

Here are two equivalent exposures...
  • micro 4/3 - 25mm, f/2.0, 1/100, ISO 100
  • full frame - 50mm f/4.0, 1/00, ISO 400
In terms of the exposure triangle, only 1 of the 3 settings remains the same (shutter speed). However, in terms of angle of view, depth of field and noise levels, the images will look the same.
Absolutely nothing to do with that conversation thread, and nobody said equivalence is gatekeeping, please read the whole thread back because we aren’t discussing equivalence at all.
This entire thread is about equivalence. It is literally in the title. No one is attacking the exposure triangle. The only complaint about the exposure triangle in this discussion is that it is a distraction/obfuscation in understanding equivalence.
 
Rather than quoting walls of text, ill pose some basic questions around the exposure triangle.

Can someone tell me, as a beginner, what is wrong with using this as a way of showing the relationship between the 3 main functions of a camera, and using it as a tool to learn how my camera works.

6b97299be4a2423db42bccb7e36263c4.jpg
It's called the "Exposure Triangle" but ISO, one of the three settings, does not directly affect exposure.

Including ISO as an exposure setting tells us that the graphic is based on a mistaken understanding of what exposure is. The underlying belief is that exposure is the lightness of the photo. That's incorrect. Exposure has been understood since the late 1800s to be the intensity of light projected by the lens upon the light-sensitive medium.

Equating exposure with image lightness leads to the flawed thinking that a photo with a pleasing lightness is correctly exposed, a photo that's too bright is overexposed and a photo that's too dark is underexposed. In the film era, there was a correlation. The film used had a specific sensitivity to light. Pairing a correct exposure with a film of a given speed would produce a negative that could easily be processed to create a print having a pleasing lightness. However digital ISO is fundamentally different.

In digital, the sensor can be any ISO that's needed. And if the ISO used in the field doesn't produce a pleasing image lightness, that can be easily adjusted in post. In fact very different exposures and ISOs can be used to make photos having exactly the same lightness.

You can see this for yourself in the DPR Studio Scene. Look at any camera in the catalog at ISO 200, ISO 6400, and at ISO 12800. All images have the same lightness but are made with substantially different exposures. The apparent lightness of a digital photo is not a reliable indicator of the exposure used.

The "Exposure Triangle" also misattributes noise in a photo to ISO. The above graphic shows noise (or grain, an irrelevant old film term) increasing as ISO increases, giving the mistaken impression that the noise we see in photos is caused by too high an ISO.

In fact, shot noise - noise that naturally occurs in light - is the predominant type of noise we see in photos. Shot noise is strictly determined by the total light used to make a photo. The only two camera settings that directly control how much light gets to the sensor are f-stop and shutter speed.

This deeply flawed graphic - which all of us were taught to rely on and reference as novice photographers - has had a real negative impact. Many photographers give far too much emphasis to ISO as the critical setting in photography. The thinking is that ISO must be kept low at all costs. If there's too much noise in a photo, it's because ISO is too high. That's just wrong.

The settings having the greatest impact on the photos we make are f-stop and shutter speed. Not only do they control important creative qualities - depth of field and rendering of motion - they determine exposure. Here's a good basic approach any photographer can take when choosing those settings:

If you use the widest aperture (smallest f-number) that produces an acceptable depth of field and the slowest shutter speed that adequately renders movement without blowing out important highlights, you've optimized exposure within your goals for the photo.

--
Bill Ferris Photography
Flagstaff, AZ
 
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It seems to me people want to rubbish the exposure triangle for nothing more than reasons of petty snobbery, to simply start an argument, or to somehow come across sas having some kind of superior knowledge, and honestly I have no idea why.
This was a thread that was answered correctly in one word in the first reply.

If everyone had left it at that, none of this would have been needed 🙂

The only reason it’s descended into this familiar exchange is that people started saying that the correct answer wasn’t. Inevitably, that invites a reasoned explanation as to why it is the correct answer. The thing is that the “exposure triangle” is a contributor to the confusion around equivalence, so as much as it is indeed a helpful thing if you want to shoot JPEGs or even convert raws to JPEGs with relatively little fuss, but when it comes to explaining equivalence it very much gets in the way.
My problem is the overall dismissal of it as a useful tool, rather than anything to do with equivalence. I understand that’s a bit off topic in this particular thread but it just annoys me when I see it being dismissed. I personally found it a really good common sense visual aide for what each setting means at its most basic level, and it allowed me (via a Brian Peterson book) to dive straight in with using manual on my first camera.

It’s been stigmatised and I can’t help but think that sometimes it’s nothing more than people sneering at it a little. Having some massively scientific explanation as to why it’s not accurate or why ISO isn’t part of the exposure is just completely missing the point of what it’s there for.
Posted at a forum member - not a moderator.

The exposure triangle is a fallacy and it gives beginners concepts that are not necessarily helpful for their growth - that they cling to instead of spending the time to learn the important concepts. It is a crutch - not a solution. There are many parallels but one that comes to mind that has done more to cause confusion is how optics was taught in college physics - particularly in engineering programs - when I was in college as an undergraduate. I had to get to my first course in quantum mechanics to learn that it geometric optics was so limited in its use that it should never be offered in the physics for physics majors. It was a classic example of teaching half truths - from the late 1890's as the physical gospel. Geometric optics was wonderful for elementary calculations and do "ray tracing." However, light does not travel in straight rays, especially through a medium, e.g., glass. It also does not bend an abrupt angles at surfaces between different medium. We have known that for over 100 years.

It took until the 1980's when Richard Feynman wrote his wonderful series of text for physics before the truth was told in the first encounter with optics at the college level. In reality, those that only care about out of camera jpegs that are bright enough don't care - they just want images that will match the output of their iPhone. When was the last time you hear a person that only uses an iPhone talk abut "the exposure triangle?"

However, the exposure triangle is now entrenched and many of those that should have moved on to understand how their camera records light - are stuck not either being able to or wanting to move on.

We often don't do beginners a favor by giving them quick fix crutches that limit their need to grow their understanding. ISO had more of a meaning in the film days. For a fixed development protocol, it related to a fixed amount of light power ( number of photons) producing a target target density as measured by densimeter. In our world of digital sensors - ISO no longer has such a meaning. It's related to brightness on processed jpegs which can be measured by three different methods - all of which give different answers.
 
It seems to me people want to rubbish the exposure triangle for nothing more than reasons of petty snobbery, to simply start an argument, or to somehow come across sas having some kind of superior knowledge, and honestly I have no idea why.
This was a thread that was answered correctly in one word in the first reply.

If everyone had left it at that, none of this would have been needed 🙂

The only reason it’s descended into this familiar exchange is that people started saying that the correct answer wasn’t. Inevitably, that invites a reasoned explanation as to why it is the correct answer. The thing is that the “exposure triangle” is a contributor to the confusion around equivalence, so as much as it is indeed a helpful thing if you want to shoot JPEGs or even convert raws to JPEGs with relatively little fuss, but when it comes to explaining equivalence it very much gets in the way.
My problem is the overall dismissal of it as a useful tool, rather than anything to do with equivalence. I understand that’s a bit off topic in this particular thread but it just annoys me when I see it being dismissed. I personally found it a really good common sense visual aide for what each setting means at its most basic level, and it allowed me (via a Brian Peterson book) to dive straight in with using manual on my first camera.

It’s been stigmatised and I can’t help but think that sometimes it’s nothing more than people sneering at it a little. Having some massively scientific explanation as to why it’s not accurate or why ISO isn’t part of the exposure is just completely missing the point of what it’s there for.
Posted at a forum member - not a moderator.

The exposure triangle is a fallacy and it gives beginners concepts that are not necessarily helpful for their growth - that they cling to instead of spending the time to learn the important concepts. It is a crutch - not a solution. There are many parallels but one that comes to mind that has done more to cause confusion is how optics was taught in college physics - particularly in engineering programs - when I was in college as an undergraduate. I had to get to my first course in quantum mechanics to learn that it geometric optics was so limited in its use that it should never be offered in the physics for physics majors. It was a classic example of teaching half truths - from the late 1890's as the physical gospel. Geometric optics was wonderful for elementary calculations and do "ray tracing." However, light does not travel in straight rays, especially through a medium, e.g., glass. It also does not bend an abrupt angles at surfaces between different medium. We have known that for over 100 years.

It took until the 1980's when Richard Feynman wrote his wonderful series of text for physics before the truth was told in the first encounter with optics at the college level. In reality, those that only care about out of camera jpegs that are bright enough don't care - they just want images that will match the output of their iPhone. When was the last time you hear a person that only uses an iPhone talk abut "the exposure triangle?"

However, the exposure triangle is now entrenched and many of those that should have moved on to understand how their camera records light - are stuck not either being able to or wanting to move on.

We often don't do beginners a favor by giving them quick fix crutches that limit their need to grow their understanding. ISO had more of a meaning in the film days. For a fixed development protocol, it related to a fixed amount of light power ( number of photons) producing a target target density as measured by densimeter. In our world of digital sensors - ISO no longer has such a meaning. It's related to brightness on processed jpegs which can be measured by three different methods - all of which give different answers.
The problem is Truman, you’re looking at this from an angle that assumes everyone wants to deep dive into the engineering and physics. 95% of people just want to go out and take photos, and be able to do it whilst controlling a camera manually. They don’t care about arguing over what ISO is actually doing, all they need to know is increasing and decreasing it has an impact on the balancing act that is getting a well exposed image with whatever creative effect you’re trying to achieve.



I can guarantee you can show that chart to a beginner, and if they have the creative ability and eye for a composition they don’t need to know any of the other fluff, they can just use that basic concept of adjusting those 3 parameters to achieve a well taken shot. And as far as they are concerned ISO plays an equal part in that.



As I said a couple of pages back, technically it might not truly impact exposure directly, but take it out of the equation (eg set it at theoretical zero) and then you won’t have an exposure to look at, it’ll be black. Then tell me how little it has to do with exposure when I’m looking at nothing on the screen.
 
Rather than quoting walls of text, ill pose some basic questions around the exposure triangle.

Can someone tell me, as a beginner, what is wrong with using this as a way of showing the relationship between the 3 main functions of a camera, and using it as a tool to learn how my camera works.

6b97299be4a2423db42bccb7e36263c4.jpg

It seems to me people want to rubbish the exposure triangle for nothing more than reasons of petty snobbery, to simply start an argument, or to somehow come across sas having some kind of superior knowledge, and honestly I have no idea why. It's a simple drawing/table that lets people understand the physical relationship between the 3 settings, and how changing one of them impacts the final image.

Set ISO to 0 and you get no exposure, increase it in line with the other 2 settings and you get an exposure. Removing it from the learning process offers nothing and claiming this 'triangle' of exposure is incorrect offers nothing.

It's a bit gatekeepery at the very least.
Equivalence is not "gatekeepery" and it is not in conflict with the exposure triangle. They are two very different concepts. I think most of the confusion in this discussion comes from people who think the exposure triangle equals equivalence.

Here are two equivalent exposures...
  • micro 4/3 - 25mm, f/2.0, 1/100, ISO 100
  • full frame - 50mm f/4.0, 1/00, ISO 400
In terms of the exposure triangle, only 1 of the 3 settings remains the same (shutter speed). However, in terms of angle of view, depth of field and noise levels, the images will look the same.
Absolutely nothing to do with that conversation thread, and nobody said equivalence is gatekeeping, please read the whole thread back because we aren’t discussing equivalence at all.
This entire thread is about equivalence. It is literally in the title. No one is attacking the exposure triangle. The only complaint about the exposure triangle in this discussion is that it is a distraction/obfuscation in understanding equivalence.
Again, you’re reading comprehension skills are lacking, you can scroll down the first page and see references to the exposure triangle. Morris brought it up, others told him the concept of it is wrong.



Please read before replying again.

--
Stu-C
 
No one is attacking the exposure triangle.
I’ll attack it if you like.

It makes no sense as a triangle. That metaphor just does not work and it’s unhelpful.

The model is three orthogonal axes: exposure time, f-number and ISO, together defining a Cartesian space in which you can combine any values of any of the three parameters. The metaphor should be a cuboid, not a triangle. (It’s not even a metaphor. It’s what it actually is.)

Excuse the appallingly crude sketch but it’s late and I can’t be bothered to do it nicely 🙂

4a45b014d1694581b31faf61e386ef51.jpg

Conveniently, this not only allows the axes to function independently as they should, but it allows you to decouple exposure from amplification.

Two of the axes (exposure time and f-number) define exposure, and thus give you one plane which can be used to describe how much light is being used to create the image. Helpfully, program lines map onto these planes of constant ISO (“isoISO” for the contour nerds) which allows a further concept to be explained.

The third axis (ISO) then takes that exposure and amplifies it, giving a brighter image.

This is how the three parameters actually interact. You start with that one plane of exposure, defined by the aperture and shutter, and that gives you light: each of those diagonal lines on the plane is a line of constant exposure. Then the third factor comes into play afterwards, by projecting that plane into a cuboid where exposure becomes multiplied by that axis to give image brightness.

To me this seems a far cleaner way of explaining it, because it’s accurate. Want to explain exposure? Use just that one plane at base ISO. Want to explain final image brightness? Start with that exposure plane and stretch it in the third axis by raising ISO. When you do that, those diagonal lines of constant exposure become planes of constant image brightness at 45 degrees to each axis.

Honestly, the triangle metaphor is simply broken whichever way you slice it.
 
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Richard Butler has written an excellent explanation of equivalence with plenty of sample images....

https://www.dpreview.com/articles/2666934640/what-is-equivalence-and-why-should-i-care
Here is a video by Simon d'Entremont, a professional wildlife and nature photographer, that covers the same subject and there are some very interesting contradictions. For example bokeh and DOF for the same lens at the same settings shot on both full frame and APS-C. Skip to 9 minutes in to see this and why I have been disagreeing.


There is a lot of agreement between the video and what Richard states yet the example of DOF and exposure with the same lens and what happens when you crop is what people here don't seem to get.

Morris
There is no contradictions, it is all physics. You just don't understand the term equivalence.

You are not allowed to redefine the term how you see fit.

It's not a controversial subject. It's very straight forward. If you don't think it's straightforward, it is a misunderstanding on your part.
 
Richard Butler has written an excellent explanation of equivalence with plenty of sample images....

https://www.dpreview.com/articles/2666934640/what-is-equivalence-and-why-should-i-care
Here is a video by Simon d'Entremont, a professional wildlife and nature photographer, that covers the same subject and there are some very interesting contradictions. For example bokeh and DOF for the same lens at the same settings shot on both full frame and APS-C. Skip to 9 minutes in to see this and why I have been disagreeing.


There is a lot of agreement between the video and what Richard states yet the example of DOF and exposure with the same lens and what happens when you crop is what people here don't seem to get.

Morris
There is no contradictions, it is all physics. You just don't understand the term equivalence.

You are not allowed to redefine the term how you see fit.

It's not a controversial subject. It's very straight forward. If you don't think it's straightforward, it is a misunderstanding on your part.
See:


There is no correct or incorrect in this case and thus I agree to disagree.

Morris
 
Here is a video by Simon d'Entremont, a professional wildlife and nature photographer, that covers the same subject and there are some very interesting contradictions. For example bokeh and DOF for the same lens at the same settings shot on both full frame and APS-C. Skip to 9 minutes in to see this and why I have been disagreeing.


There is a lot of agreement between the video and what Richard states yet the example of DOF and exposure with the same lens and what happens when you crop is what people here don't seem to get.
I only watched about two minutes from the suggested point. First he tries to demonstrate equivalence by using the same focal length and aperture on two sensor sizes and ends up with two differently framed images. Helpful. Then he crops one to the size of the other as if that’s equivalent (it’s not, it’s just the exact same thing). Then there’s the comedy gold where he says “small sensors make us stand farther back … larger sensors make us get closer to our subject”. Er… not even sure what to say to that.
 
Here is a video by Simon d'Entremont, a professional wildlife and nature photographer, that covers the same subject and there are some very interesting contradictions. For example bokeh and DOF for the same lens at the same settings shot on both full frame and APS-C. Skip to 9 minutes in to see this and why I have been disagreeing.


There is a lot of agreement between the video and what Richard states yet the example of DOF and exposure with the same lens and what happens when you crop is what people here don't seem to get.
I only watched about two minutes from the suggested point. First he tries to demonstrate equivalence by using the same focal length and aperture on two sensor sizes and ends up with two differently framed images. Helpful. Then he crops one to the size of the other as if that’s equivalent (it’s not, it’s just the exact same thing). Then there’s the comedy gold where he says “small sensors make us stand farther back … larger sensors make us get closer to our subject”. Er… not even sure what to say to that.
So the cropped image did not appear the same?

Morris
 
So the cropped image did not appear the same?
Same as what?
The same as the APS-C image.
Of course it’s the same! It is identical. It is the same area of the same projected image from the same lens at the same focal length and the same aperture.

That’s not equivalence, it’s identity.

But your original comment around cropping was different. You were suggesting that DoF does not change when you crop an image:
if you take a photo with a 24mm f/2.8 lens on a 35mm sensor. Then you print it and cut off the part that would be cropped by an APS-C sensor, did the depth of field change?
This is a comparison not between the APS-C crop and the APS-C sensor (which are the same thing) but between any image and a crop of that image. The reason depth of field changes during cropping is due to the change in size of the circle of confusion, which is a component of depth of field.
 
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