The fallacy of 35mm "equivalent focal lengths"

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Tony Beach Forum Pro • Posts: 11,967
The fallacy of 35mm "equivalent focal lengths"
7

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.

Donald B
Donald B Forum Pro • Posts: 12,774
Re: The fallacy of 35mm "equivalent focal lengths"
1

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

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Sranang Boi Senior Member • Posts: 1,833
Re: The fallacy of 35mm "equivalent focal lengths"
16

I feel sorry for you. It must have taken quite some time to type all that. If only it was accurate you would have been onto something.

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jrtrent Veteran Member • Posts: 5,076
Re: The fallacy of 35mm "equivalent focal lengths"
18

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.

OP Tony Beach Forum Pro • Posts: 11,967
Re: The fallacy of 35mm "equivalent focal lengths"
2

Donald B wrote:

nothing wrong with good quality small cameras

I didn't say there was. Indeed, part of what I wrote about is equivalence, and that's a two-edged sword -- so on the one hand you need ever smaller focal numbers (so using f/2 on a 50mm lens is the same as using f/1 on a 25mm lens) but on the other hand when you stop down a larger lens on a larger format you are essentially staying even with what can be done on a smaller lens on a smaller format (so using f/2 on a 25mm lens is equivalent to using f/4 on a 50mm lens).

Buried in all that text I did say I should be able to get more reach with the sub $400 camera that I am getting my girlfriend versus the thousands of dollars I have spent on my D800 and lenses. The fallacy I was writing about is that any lens, really on any format (even on 35mm) has an equivalent focal length that can be defined by anything other than its FOV on the format its being used on.

OP Tony Beach Forum Pro • Posts: 11,967
Re: The fallacy of 35mm "equivalent focal lengths"
2

Sranang Boi wrote:

I feel sorry for you.

Oh please, don't, but then I'm sure you aren't.

It must have taken quite some time to type all that. If only it was accurate you would have been onto something.

Feel free to demonstrate how and where what I wrote and showed is wrong. I'm waiting.

OP Tony Beach Forum Pro • Posts: 11,967
Re: The fallacy of 35mm "equivalent focal lengths"
2

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.

TonyGamble Veteran Member • Posts: 3,066
Re: The fallacy of 35mm "equivalent focal lengths"
2

Then apparently you stopped reading after the first paragraph.

I did Tony.

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

Tony G - London

threw the lens
threw the lens Contributing Member • Posts: 955
Re: The fallacy of 35mm "equivalent focal lengths"
8

I wonder what it is about equivalence that brings out long disquisitions that demand they must be heard.

Not on the level of Kierkegaard is it?

jrtrent Veteran Member • Posts: 5,076
Re: The fallacy of 35mm "equivalent focal lengths"
7

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.

I read the whole thing, I just disagree with you that optical resolution, pixel density, and aperture diameter have anything to do with equivalent 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.  I compose in the viewfinder and do not crop my images later.

OP Tony Beach Forum Pro • Posts: 11,967
Re: The fallacy of 35mm "equivalent focal lengths"

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.

I suggested in the second paragraph to skip to the picture:

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).

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).

mamallama
mamallama Forum Pro • Posts: 55,565
Re: The fallacy of 35mm "equivalent focal lengths"
3

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.

I suggested in the second paragraph to skip to the picture:

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

Provide a concise precise technical definition of equivalent as you are using the term. That will save a lot of the round robin discussions that have taken place.

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).

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).

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Gerry Winterbourne Forum Pro • Posts: 15,905
Re: The fallacy of equating "focal length" with "reach"
13

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.

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.

[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.

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___________________________________________
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gerry.winterbourne@ntlworld.com

OP Tony Beach Forum Pro • Posts: 11,967
Re: The fallacy of 35mm "equivalent focal lengths"

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.

I read the whole thing,

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. Changing the focal length to achieve that has ramifications for image quality as well as DOF. As I wrote in the OP, for many it's not a big deal, so if that includes you then you're done here.

I compose in the viewfinder and do not crop my images later.

So I'm sitting with my girlfriend at an Agility event and she sees a coyote on the hill and wants me to get a photo of it (this actually happened). Do I use the S95 I have in my pocket that I mostly use to shoot videos of her running her dogs, or do I use the 85mm lens sitting on my D800 that's sitting nearby? If you believe the marketing the compact camera is the better tool, but the marketing is often fallacious.

OP Tony Beach Forum Pro • Posts: 11,967
Re: The fallacy of 35mm "equivalent focal lengths"

threw the lens wrote:

I wonder what it is about equivalence that brings out long disquisitions that demand they must be heard.

There is no demand from me, which makes me wonder why some feel compelled to read what they don't want to read (or feign doing so) and then post something snarky about it.

OP Tony Beach Forum Pro • Posts: 11,967
Re: The fallacy of 35mm "equivalent focal lengths"

mamallama wrote:

Tony Beach wrote:

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

Provide a concise precise technical definition of equivalent as you are using the term. That will save a lot of the round robin discussions that have taken place.

I just did. It's more accurate to say a focal length when used on a particular format has a particular FOV.

OP Tony Beach Forum Pro • Posts: 11,967
Re: The fallacy of equating "focal length" with "reach"

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.

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

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.

threw the lens
threw the lens Contributing Member • Posts: 955
Re: The fallacy of 35mm "equivalent focal lengths"
1

Tony Beach wrote:

threw the lens wrote:

I wonder what it is about equivalence that brings out long disquisitions that demand they must be heard.

There is no demand from me, which makes me wonder why some feel compelled to read what they don't want to read (or feign doing so) and then post something snarky about it.

It seems to me that with you rounding on all comers, a Thread Lock is almost inevitable here.

mamallama
mamallama Forum Pro • Posts: 55,565
Re: The fallacy of 35mm "equivalent focal lengths"
11

Tony Beach wrote:

mamallama wrote:

Tony Beach wrote:

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

Provide a concise precise technical definition of equivalent as you are using the term. That will save a lot of the round robin discussions that have taken place.

I just did.

Where? If you have already stated it then copy and paste the precise definition of equivalent here.

It's more accurate to say a focal length when used on a particular format has a particular FOV.

Our learned folks here at DPR use the term equivalent focal length in discussions and in their lens specifications. They are very definite in the definition of how they are using the term equivalent. It is not a fallacy. It is how the whole industry uses the term.

Now you are coming along claiming it is a fallacy. That is why I want to know your definition of the term.

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RedFox88 Forum Pro • Posts: 29,205
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