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:
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.
