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01-25-2019, 02:34 AM   #31
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I agree that the lenses shouldn't have "pseudo-focal-lengths" like that printed on them that vary according to the format they are intended for, that would just confuse things, but perhaps an additional FOV printed on them (with a format suffix) would help I think. Sure I have no problem with FF/apcs-c/m43, but when compacts or phones with different hard-to-find-sensor-sizes say that the lens is a 3-18mm lens...that doesn't really help me at all to get a feel for what to expect.

(But I guess this post isn't about equivalence but more about what's printed on the lens....)

01-25-2019, 02:35 AM   #32
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QuoteOriginally posted by swanlefitte Quote
Focal length is the distance from the axis of the lens to the plane it is sharp at infinity focus. That is still 18-50mm, that doesn't change. On ff or apsc the lens is just as far from the sensor.
And that is what I mean that people should think more about the image circle and the fact it hasn't changed between formats.
And it helps with one other issue about "equivalence" that people often don't get and that is the things that don't change between formats. For instance the exposure value doesn't change.
01-25-2019, 02:36 AM - 1 Like   #33
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The fundamental problem is depth-of-field onanists.
The rest of us, like you, care about angle of view, perspective, and exposure.
01-25-2019, 03:13 AM - 1 Like   #34
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Thanks for all the interesting and very civilised responses thus far, folks!

QuoteOriginally posted by photoptimist Quote
Given that photographers are often exposed to images taken in different formats and may even own cameras with different formats, equivalence helps them relate focal length and aperture choices across formats. And if they are shopping for a new system, equivalence helps them spec nearly apples-to-apples alternatives across formats.
Exactly. This is the crux of how I (rightly or wrongly) understand and use equivalence.

As I mentioned previously, I've been using APS-C and full frame cameras side by side for long enough that I now don't think about equivalence much - or, if I do, I'm not conscious of the fact. But it was a useful concept to me earlier in my photography, and I'm certain I still use it occasionally without realising it

QuoteOriginally posted by reh321 Quote
My issue with your explanation is that your "artistic" use case has virtually no connection with how I typically take photos - so let me describe an actual situation.

<snip>

In my use case, I'm making decisions "on the spot", and typically not basing decisions {other than ISO and shutter speed} on some previous effort; even if you had been standing next to me with a K-1, we wouldn't have had time to exchange information, let alone to calculate equivalences.
Right. And in this specific use case, I'd concur there's little value in thinking about equivalence. We're not compelled to use it in every scenario. More often, we use what we have and make that work.

QuoteOriginally posted by normhead Quote
If you have a zoom lens why do you need equivalence. A pretty typical use, Zoom the 60-250 to the framing I want.

Check the focal length.
DO I have a prime close to that in my camera bag?

1. Yes, maybe switch to prime.
2. No. Stay with the 60 -250.

Put the 60-250 on the K-1 and repeat.

No math involved.
Sure, and that's a great way to work. But it doesn't negate the potential value of calculating equivalent focal length and aperture settings in other circumstances. Again, it's a use case thing. We use whatever approach works for us in a particular situation.

QuoteOriginally posted by normhead Quote
No one is saying equivalence is worthless. But, it's possible to learn everything you need to know, other ways. Equivalence is overshadowed by more useful concepts.
It's not a panacea, that's for sure. All I'm suggesting is that there are situations where it can be useful. There's a tendency to demonise it, when understood and used correctly it can have value - for some folks, at least. Those that don't find it useful are free to do things using their preferred approach

QuoteOriginally posted by photoptimist Quote
And yet the classic "f/8 and be there" rule varies with the format.

An APS-C user would say "f/5.6 and be there," an M43rds user would say "f/4 and be there," and a 8x10 user would say "f/64 and be there (with a big tripod)."
In a related use case of mine, a few years back I became interested in the (now late) Bill Cunningham's work, equipment and technique. On his 35mm film cameras, I found out that he most frequently used a 35mm lens set to f/8, and pre-focused to the approximate distance where he expected his subjects to cross his path. Classic street photography stuff. Using my definition of equivalence, I knew that a 24mm lens at f/5.6 would give me roughly the same field of view and depth of field on my APS-C kit. That was enough to get me started in trying out his style of photography. Sadly, it didn't give me his confidence, patience, eye for interesting human subjects or easy access to 57th and 5th in NYC

QuoteOriginally posted by reh321 Quote
But none of this matters for some of us.
Acknowledged. But for those where it matters, I maintain that focal length and depth of field equivalence can be a useful concept.

QuoteOriginally posted by reh321 Quote
Most people never memorized the 35mm rules, so those who care about DOF will carry a DOF calculator around with them; I see little use for worrying about equivalence.
Sure, but even now, with many different sensor formats in frequent use, field of view and depth of field discussions are typically standardised around 35mm "full frame" format - presumably because this was the most widespread and accessible format for many decades.

If you don't need or care about equivalence, that's great. There's no sense in introducing it to your thought process if you have no need of it

QuoteOriginally posted by garywakeling Quote
A concise and easy to follow explanation, how dare you make the topic so easily understood, how will keyboard warriors use their time now? Oh well, time to sit back and watch, Thanks
Thank you It's a nice thread so far with very positive contributions. I never expected us all to agree - quite the contrary. It's interesting to see what others think, as well as how unpopular the concept is with some folks

QuoteOriginally posted by Fogel70 Quote
No matter what method you use, if you get the relations correct, you have learnt the equivalency between the formats.

The mathematical method is usually the quickest an most simple way to learn about equivalency, because the calculations are so simple.
Yep. That's my take on it

QuoteOriginally posted by biz-engineer Quote
There is no such thing as equivalence because I tell the difference of two prints from apsc and medium format cameras, no need to even look close, the medium format wins on latitude and tone definition. Medium format is bigger, more expensive and deliver better images, so it's not at all equivalent to other formats.
This is a difference in how you and I define equivalence. And it probably highlights the inaccuracy or inadequacy of the word in describing the concept. This is why, in my original post, I asked folks not to get too hung up on the word but to embrace the concept I was describing - to wit, "the focal length and aperture setting relationship between lenses used on different format cameras in order to achieve results that are comparable in field of view and depth of field, for identically-composed shots taken at the same camera-to-subject distance".

QuoteOriginally posted by beholder3 Quote
And everyone understanding "equivalency" knows that DoF and background blur are not in sync in any way. Down to the point that in more than enough cases one combo will have "shallower DoF" and the other will have "more background blur".
Acknowledged. Though equivalence can still get someone "in the ball park" in terms of the level of background blur. They can fine tune from there.

QuoteOriginally posted by Sandy Hancock Quote
The fundamental problem is depth-of-field onanists.
The rest of us, like you, care about angle of view, perspective, and exposure.
That's a tad harsh (funny, though) But depth of field can be pretty important depending on what you're shooting. Take the landscape photographer with his wide angle lens who wants as much of the scene as possible to be acceptably sharp. Or the artsy portrait photographer who wants the "one eye in focus" look that @photoptimist referred to. When switching between formats - either because you use different cameras, or you're switching to different kit, or maybe you've just read an article where the author used a particular format and lens - equivalence (as I've described it) can potentially help.


Last edited by BigMackCam; 01-25-2019 at 03:32 AM.
01-25-2019, 04:00 AM - 1 Like   #35
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I think the big thing that equivalence does is it helps one to understand how focal lengths will behave on different sensor cameras. This is probably most useful when you are moving from one size sensor to another. I shot APS-C only for years and when I got a K-1, I did have to think about the field of view focal lengths would show on the K-1 versus my K3 and K-01 and how much I needed to stop down to get adequate depth of field for my image. And yes, in the beginning I would shoot at f5.6 or f8 on the K-1 and wouldn't be happy because there wasn't enough depth of field for my taste.

I learned over time and I don't think about it much anymore, but if I would buy a 645z at some point, I would need to go through this again and it would be helpful to me.

I do think the equation is important to think about because it does explain that to have a similar image you need to adjust focal length, aperture, and iso. Most people just pay attention to the focal length 50mm on APS-C = 75mm on full frame, and leave it at that, but there is a bit more.

Equivalence does not say that one format is best and shouldn't be used to explain why one camera is better than others. I also see it as problematic because most people talk about lenses at their widest: "I don't like APS-C because I can't find an equivalent lens to my FA 50 f1.4." By which they mean that they need an APS-C lens that is 30-ish mm and f0.9 or some such animal that doesn't exist. But if you mainly shoot stopped down then this is not a problem at all and you could easily use the DA 35 macro or FA 35 or FA 31 limited to satisfy your need. Just because a lens has a wide maximum aperture doesn't mean that it is particularly usable there and most of us would do well to stop down a bit for better sharpness.

Thanks for making this thread, Mike. I know it is a bit controversial and for most of us on the Forum, equivalence isn't even very helpful -- we do these calculations without even thinking about them, but it does get confusing for a lot of new photographers, particularly when they are moving between formats.

Last edited by Rondec; 01-25-2019 at 04:07 AM.
01-25-2019, 04:35 AM   #36
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35mm equivalence is useful to select lens focal length relative to the kind of viewing angle we are looking for. But the theory that larger sensor isn't better is shown to be flawed by simply comparing a medium format image with the same image taken with a phone, and seeing the evidence that the medium format image is clearly better than the image from the phone. However, camera systems with larger sensors tend to be more expensive, even much more expensive, and that is why sometimes equivalence provides emotional soothing when we don't have the budget for the big system. Usage of smaller print/viewing enlargement is a better argument for limited budget than trying to use equivalence. Practically, if portability is an issue, and the print is made into product catalog and magazines and web media, the smaller system is the right choice: no need to use equivalence to say that the smaller system deliver equivalent IQ, because it's not true.
01-25-2019, 04:42 AM - 1 Like   #37
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The math is great, but it doesn't have to be complicated. A picture says a thousand words.
For any given focal length, this is the "equivalence":



It may get complicated with the sensor technology between the format size, but all things equivalent, then it is much easier to conceptualise.

This is a nice simplified explanation of the difference that the sensor size makes on "equivalence":
Mark David | APS-C vs full frame

Then for the geeks this is the article for you:
Full Frame vs
01-25-2019, 04:45 AM   #38
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QuoteOriginally posted by Ash Quote
The math is great
I can see how to proceed with the apsc and full frame. However how do you calculate the equivalence for the circular aspect ratio?

01-25-2019, 04:47 AM   #39
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QuoteOriginally posted by biz-engineer Quote
35mm equivalence is useful to select lens focal length relative to the kind of viewing angle we are looking for.
Yes, and it's useful for understanding roughly what aperture you might need to achieve similar depth of field, if that creative aspect is important to the use case.

QuoteOriginally posted by biz-engineer Quote
But the theory that larger sensor isn't better is shown to be flawed by simply comparing a medium format image with the same image taken with a phone, and seeing the evidence that the medium format image is clearly better than the image from the phone. However, camera systems with larger sensors tend to be more expensive, even much more expensive, and that is why sometimes equivalence provides emotional soothing when we don't have the budget for the big system. Usage of smaller print/viewing enlargement is a better argument for limited budget than trying to use equivalence. Practically, if portability is an issue, and the print is made into product catalog and magazines and web media, the smaller system is the right choice: no need to use equivalence to say that the smaller system deliver equivalent IQ, because it's not true.
This is why I steer clear of stating that the images obtained from different cameras using lenses of equivalent field of view and aperture setting will be identical. I narrowly limit my definition of equivalence to field of view and depth of field... There are so many other factors at play that to achieve absolute equivalence in every aspect of an image would be impossible
01-25-2019, 04:54 AM - 1 Like   #40
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Equivalence considered harmful

Challenge accepted.

First thing first:
What is "equivalence"?
As Mike noted, the heated discussions around "equivalence" is due to it being misunderstood. Unlike Mike, I'd argue that its advocates do not understand it in the first place. So, what is this "equivalence" thing?

Is it trigonometry? Some advocates assumes so, when claiming that one would revert to trial and error if avoiding the wonder called "equivalence". Obviously, that's nonsense. Trust me on this: trigonometry didn't wait for Joseph James to be invented; it's more than 2 millennia old. Any claim that "equivalence" encompasses the basic mathematical apparatus it's using is absolutely bonkers.

Something else that's entirely bonkers is trying to explain "equivalence" in (almost) 50,000 words. Yet "you didn't read the article!" is a common theme of these advocates (FTR, I did read it).
What good a system which needs 50,000 words to be explained? I'll do "equivalence" a favor and reject that as a definition for now - it is a lame attempt, at appearing an expert on the author side, and at grossly overreaching on the "equivalence" side.

I'll thus go with Mike's elegant, simple description:
QuoteOriginally posted by BigMackCam Quote
For me, "equivalence" describes the focal length and aperture setting relationship between lenses used on different format cameras in order to achieve results that are comparable in field of view and depth of field, for identically-composed shots taken at the same camera-to-subject distance.
Excellent! - and I'm not sarcastic. We have a common starting point.
Now comes the difficult part: properly understanding such a simple definition.
- computing the angle of view by itself is not "equivalence", it's trigonometry. Computing DoF is not "equivalence". You can have all those without "equivalence", just not put together in this very specific way.
- all "equivalence" does is telling you, "focal length F1 and aperture A1 on format X1 gives you a similar field of view as focal length F2 and aperture A2 on format X2, if everything else remains constant". Nothing more than that. This is very important, and leads us to the following point.

When is "equivalence" useful?
If you say anything other than "when you want to precisely match both field of view and DoF from a format on another, everything else remaining constant", you haven't been paying attention.
Now, answer honestly: when was the last time you
a. wanted to precisely match a photograph taken with a different format, in field of view and DoF but no other aspect
b. had all the necessary information and was able to match the shooting conditions, relevant processing down to the final display media?

"I need focal lengths roughly 1.5 times longer on this format" isn't "equivalence", is an useful rule of thumb (one backed by trigonometry, but you don't need its precision). "I need to close down the aperture a bit more on this format" isn't "equivalence" either. Both can be explained in at most 5 minutes.
And if you really do need precision, you're way better served by knowing the basic optics and mathematical apparatus - and apply it directly. You can do much more than getting the same FoV and DoF, and you can do only what you actually need. Knowledge, not mechanical application of a predefined template.

When is "equivalence" utterly useless?
This is something that escapes "equivalence"'s advocates; in the first place, it is utterly useless when you don't want to reproduce field of view and DoF from a format to another.

Fact: most people are using a single format. They couldn't care less about reproducing FoV and DoF, because there's no format they're attempting to emulate. All these "you're an APS-C user, your 35mm lens is like a 50mm on FF"? It doesn't help at all - actually it hurts a lot - because they have no clue what a 50mm looks like on FF, and don't even care.

Fact: "equivalence" breaks at a sneeze. You have to keep everything but focal length and aperture the same, or else its formula will no longer work. Crop - it breaks. Take a step closer - it breaks. Print larger - it breaks. Not being able to buy a precisely "equivalent" lens - it breaks. Blink the wrong way - it breaks.
If it's the 50,000 word definition, that's broken by default because it implies some imaginary sensors and stuff.
Wait, that's not all: "equivalence" breaks as you decide to do something different, as you decide to explore the new format and use it better. "I can do this now" doesn't work with "equivalence".

The entire premise of choosing lenses primarily on angles of view and especially DoF is absurd. There are so many other aspects, even subjective ones like rendering... as for composing and DoF, you have quite a bit of freedom and control there, outside the rigid "sit in that precise spot with the camera pointed out in that precise direction".
Aperture itself is not a mere DoF control mechanism. Stopping down 1-2 stops on a lens which isn't that sharp wide open; to hide AF's imprecision; opening up more than you'd want because there is no light - there are many other reasons for choosing a specific F-stop, and what works on a camera won't necessarily work in an identical manner on another.

We're photographers, not photocopiers.

A bit of background
Nobody needed "equivalence" during the golden days of photography - when people still put some effort to learn the craft, rather than flipping their smartphones around filling the Internet with pictures of their lunches.
Why now, in the digital age? If you're not a millennial, you probably know we had tons of formats during the film age (more than the usual digital formats). Perhaps well intended gentlemen tried a simpler way of explaining basic concepts to beginners?

Yeah, right.
It indeed started as an attempt to hide the most basic concept in optics: focal length. Targeted at point&shoot users, who didn't even knew their digital toy's sensor size and could only use the "focal length" as a replacement for angle of view. It was wrong, but it worked to some extent.

This was still a "partial equivalence". Its full form appeared as a tool to explain how "full frame" is better - particularly to people using "lesser" formats. Indeed, this is a tool for silly Internet arguments.
Even now, you cannot use "equivalence" without coming to the conclusion that the "full frame" format is inherently superior. Or you can use the "partial equivalence" to claim a smaller format is "better", that's what Olympus is doing.

Equivalence considered harmful
The result - of enforcing the rigid system of "equivalence" on people for whom it doesn't work (see the point about single system users) was inevitable: confusion.
People stopped knowing what focal length is (despite - I assume - learning basic optics in high-school or university). APS-C-only users trying to think about different lenses on formats they never used, trying to solve invented problems. Yes, the 50mm is a 50mm. Yes, cropping works the same regardless how you're doing it.

How many times I've heard an APS-C-only user wondering, what will happen if he put a - say - 50mm FF lens on his camera? What focal length would it become? Not at all comparable with the long end of his 18-55, right?
Usually the responses fall into 2 categories: people like myself would explain to him how the focal length is a basic optical concepts completely independent on the camera, so a 50mm will be a 50mm. Nothing to worry about.
"Equivalence" advocates often start by explaining their much beloved system, completely missing the point - that the user doesn't want to reproduce FF results on APS-C; all he want is to use the lens. And the confusion deepens.

I will urge you to read post #27 - the proposal to inscribe fake focal lengths on lenses. That guy with a YouTube channel - Tony Northrup - said the same, even accusing lens manufacturers of not doing it.
What a nightmare would that be! With a fixed lens that will sort of work, but not with an ILC:
- the existing lenses have correct focal length values inscribed. So you will have to differentiate between fake and correct lenses, let's say by the lens' name (say, DA-E ), a colored ring on the fake, and some note on a website. How on Earth would that simplify anything?
- with Pentax, you can put APS-C lenses on the K-1; and they just work. Even more, you don't have to crop to APS-C; actually some APS-C lenses can be used in FF mode, while with others you can just crop a little bit. Imagine the DA* 300mm being inscribed as DA* 450mm. Now explain why it isn't as long as the D FA 140-450mm.
- how about the square crop mode? What "focal length" is that? What if you switch the K-1 to APS-C mode, you will no longer get the same results as a "fake" lens on an APS-C camera. You cannot link "focal length" with cropping (actual frame size), unless you stop cropping at all.

Last but not least: folks, the metric system is a standard!
Don't mess up with it, unless you're fine to buy "equivalent kg" of groceries, fuel your tank with "equivalent l" of gasoline, and so on.
01-25-2019, 04:54 AM   #41
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QuoteOriginally posted by Ash Quote
The math is great, but it doesn't have to be complicated. A picture says a thousand words.
For any given focal length, this is the "equivalence":
That's a great illustration, and extremely helpful in understanding the cropping effect that different sensor sizes have when used with the same lens. But it has it's own problems... A new photographer looks at this and now realises why his M50mm f/1.7 lens (a fast fifty that everyone says everyone else should own) doesn't give him much room to work with when fitted to his K-50. His natural tendency would be to step back so that the subject fills the frame to the extent he wants. But that's not always possible, and he's now introduced a different perspective. If he understood equivalence, he'd know that he'd be better off with a 35mm lens instead of the fast fifty all those 35mm film and full frame photographers rave about
01-25-2019, 04:58 AM   #42
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QuoteOriginally posted by reh321 Quote
Most people never memorized the 35mm rules, so those who care about DOF will carry a DOF calculator around with them; I see little use for worrying about equivalence.
I was using 35mm film before I switched to APS-C digital and now I'm with 35mm digital.
I don't need any "equivalence". I never attempted to replicate the old format look, rather to discover new format's.

Pushing "equivalence" on APS-C only users is complete nonsense.
01-25-2019, 05:29 AM   #43
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QuoteOriginally posted by Fogel70 Quote
The main difference between case A and B is that perspective change in case B, but is constant in case A.
Changed perspective is not really about equivalence, as constant perspective is part of equivalence.
I dont agree. A very typical question is driven by constant framing: "I want to shoot a bird in flight filling the frame, which lens do I need and what will the result look like from noise perspective"

I also would not agree to the fundamental assumption you make that "perspective" changes with field of view. In my knowledge of definitions "perspective" just governs the questions "from where do I look" and "to where do I look". This is separate from field of view.

---------- Post added 25th Jan 2019 at 13:31 ----------

QuoteOriginally posted by BigMackCam Quote
That's a great illustration, and extremely helpful in understanding the cropping effect that different sensor sizes have when used with the same lens. But it has it's own problems... A new photographer looks at this and now realises why his M50mm f/1.7 lens (a fast fifty that everyone says everyone else should own) doesn't give him much room to work with when fitted to his K-50. His natural tendency would be to step back so that the subject fills the frame to the extent he wants. But that's not always possible, and he's now introduced a different perspective. If he understood equivalence, he'd know that he'd be better off with a 35mm lens instead of the fast fifty all those 35mm film and full frame photographers rave about
That is exactly the point I was making above with my preferred case of constant framing of the main subject. To me subject distance is a variable I'll adjust in the interesting cases for equivalency.
01-25-2019, 05:59 AM   #44
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QuoteOriginally posted by biz-engineer Quote
I can see how to proceed with the apsc and full frame. However how do you calculate the equivalence for the circular aspect ratio?


I would go with calculating it from the largest quadrilateral aspect you can for within the lensís circular projection. Usually that would be with a 3:2 ratio as per the common sensor sizes. But Iím guessing your question relates more to lens properties, and I personally do not know how lens focal length calculations are made. I leave that to experts in the field: http://www.giangrandi.ch/optics/focalcalc/focalcalc.shtml


01-25-2019, 06:02 AM   #45
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QuoteOriginally posted by BigMackCam Quote
Depth of field can be pretty important depending on what you're shooting. Take the landscape photographer with his wide angle lens who wants as much of the scene as possible to be acceptably sharp. Or the artsy portrait photographer who wants the "one eye in focus" look that @photoptimist referred to. When switching between formats - either because you use different cameras, or you're switching to different kit, or maybe you've just read an article where the author used a particular format and lens - equivalence (as I've described it) can potentially help.
....or not help.

The first situation you describe (landscape with everything in focus) would theoretically be be better served with a tiny sensor where the shorter equivalent focal length would provide much greater depth of field for a given field of view. I think we all know the limitations of that approach.

The second situation (one eye in focus) would ideally be achieved with a medium or large format camera, but for all sorts of reasons the lenses with the shallowest depth of field have been developed for the 135/FX/35mm format. Generally speaking, medium (and larger) format lenses are sufficiently slower to negate any depth of field advantage they may have offered for the equivalent angle of view and perspective.

Understanding equivalence is fine. Putting it into practice is more complicated.
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