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01-24-2019, 02:48 PM - 12 Likes   #1
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"Equivalence" between formats and lenses...

From time-to-time - certainly not infrequently - the subject of "equivalence" comes up in these forums. It's raised for a variety of reasons, often based on significant misunderstanding, e.g. "If I use a 50mm full frame lens on my K-30, is it now a 75mm lens?".

This subject always generates a significant amount of heated conversation, which seems to become more-or-less polarised between two camps - those that think equivalence is a misnomer and / or of no practical use, and those who maintain the opposite (with a few folks in the middle ground between).

Indeed, this very discussion once again developed in a recent thread, the original subject of which had nothing to do with equivalence, so I thought I'd start a new thread to discuss this. Those who've heard it all before and want no part of this, please ignore. For the rest, please let me know your thoughts on what follows. Every one of our more experienced members I've spoken to about this has good, valid arguments, and I respect all opinions. I can't promise to agree with them, but if I disagree, it'll be respectful... so I hope each of you will extend the same courtesy to me and others who respond. Sound good?

What is "equivalence"?


This is where a lot of the debate and argument starts, I believe, because different folks have subtly or wildly different views on what "equivalence" means in this context. For now, I ask you not to get hung up on the word, but to hear me out on what I think we're talking about - or, more accurately, what it means to me

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.

An example:

Two friends are shooting potraits of the same model in a small studio, from the same distance. Friend #1, the more experienced of the two, has his trusty full frame K-1 with FA77 f/1.8 Limited lens, and is shooting at f/4. Friend #2, quite inexperienced, likes the results his buddy is getting in terms of framing and background blur - but he "only" has an APS-C cropped sensor K-50. What lens and aperture setting must he use to get approximately the same field of view and depth of field? The more experienced friend knows that, using commonly-espoused and well-worn calculations:

target_format_focal_length = full_frame_focal_length / crop_factor

and

target_format_aperture = full_frame_aperture / crop_factor

Since the crop factor for the K-50 compared to the K-1 is roughly 1.5, he can calculate:

Required focal length = 77 / 1.5 = 51.333 (so, let's say 50mm)

and

Required aperture = 4 / 1.5 = 2.667 (so, let's say f/2.5 or perhaps f/2.8)

Knowing this, he tells friend #2 to grab his old FA50 f/1.4 from his bag, fit it to his camera and set the aperture to f/2.8. In doing so, he will approximate (not replicate, but approximate) the field of view and depth of field that his buddy is getting with the K-1 and FA77 at f/4.

Now, I realise that the lenses are different. They render very differently, and the performance of an FA50 f/1.4 at f/2.8 will be completely different and relatively poor compared to the FA77 at f/4... the resolution, even the colour, contrast and character of the bokeh will be different... but the point here is, the field of view and depth of field will be quite similar.

Will the resulting images be absolutely "equivalent"? Of course not. But the field of view and depth of field will be approximately equivalent.

This is my personal understanding of "equivalence". I appreciate others will differ and disagree (perhaps strongly), and that's fine. But this is the foundation from which I discuss and debate the topic.

So, why can the concept of "equivalence" (as described) be useful?

I could fill an entire thread with reasons why my concept of equivalence might be useful, but let's take a common example that we see on these forums time and time again, and extend it a little:

A new member, 35mm film shooter in his past, buys a K-50 and wants to use his old K-mount lenses. But he's seeing things differently when he pairs those lenses with the K-50. He has to stand back much further, and things still don't look quite right.

Now, we explain to him that this is because the sensor is cropped, so it captures less of the image circle projected by the lens. His M50 f/1.7 is still a 50mm lens, but the outer portions of the 35mm frame have been cropped away.

So, how can he use his collection of K-mount glass effectively? Well, using the concept of equivalence (as I understand it), we can tell him that a 35mm lens will offer him roughly the same field of view on his K-50 as the M50 f/1.7 did on his old ME Super. So, based on recommendations, he buys an inexpensive "plastic fantastic" DA35 f/2.4 and starts shooting with that. Initially he's pleased...

... and then he comes back, confused because he can't achieve the same shallow depth of field he got when shooting the M50 f/1.7 at f/2.8.

"Ah," we say, "you'd need a 35mm lens with a maximum aperture of at least f/1.8 to get that same depth of field". And then we explain why, using the calculations I stated above.

He's dejected now, as he can't afford such a fast 35mm lens - but at least he knows that's what he needs, or more likely, the limitations he'll have to accept based on his choice of format.

Let's take a completely different - but equally valid - example:

A forum member with little recent experience has jumped right in and bought a K-1 without thinking of the implications (we've seen that many times here on the forums). And guess what? He wants to take wildlife photos at long distances.

He's got a nice old SMC Pentax-M* 300mm F4 that he bought on eBay. Should be plenty long enough, right? Except that, compared to his friends, the birds and deer in his photos look much further away.

It turns out that his friends - seasoned specialist wildlife photographers - made the (arguably) smart choice for this use case and picked high-resolution cropped format cameras. So now we tell him that, if he used that same lens on a K-3, he'd be all set.

"Well, that's great" he says... "but how can I get those results on the K-1 I just shelled out my monthly mortgage payment on?". And we explain the equivalence calculations - at least, the focal length part - so he understands that he will need a prime or zoom capable of 450mm or thereabouts. Either that, or he'll have to crop, and that will give him considerably reduced resolution. The choice is his.

Why has my understanding of "equivalence" helped me?

Much of my early photography learning, and some of it still, was based on looking at other peoples' photos and understanding how they took them, or reading about the equipment folks choose to cover their use cases.

A lot of what I read (both in the past and present tense) relates to 35mm film or full frame digital photography. For some years, though, I was shooting only cropped sensor APS-C format cameras. Yet I wanted to know how I could recreate many of the results I saw in others' photography.

Here, the concept of equivalence was a huge benefit to me, although it took me quite a while to process and discard the mis-information and understand it properly.

When I did understand it, I quickly realised that for day to day shooting most 35mm guys would perform with a "normal" 50mm lens, I'd need to use something in the 30 - 35mm range. And if I wanted the same shallow depth of field, I'd need something much faster than they were using. I realised that the 24-70 f/2.8 and 70-200 f/2.8 "do-it-all" kit could be replicated with a 17-50 f/2.8 and 60-250 f/4, albeit with some differences in field of view and magnification at the limits, and a considerable difference in the minimum depth of field achievable.

Then I bought a full frame camera and those very lenses I'd used "equivalence" to emulate. The results were pretty much as expected, except that I revelled in the ability to achieve much shallower depth of field (read "subject isolation") with even quite humble lenses. But then, when I wanted to shoot longer distance subjects, I had to invest in considerably longer focal length lenses to achieve the same framing, whilst having to stop down further to get the same depth of field.

But I knew all of this, because I already understood (however flawed) my concept of "equivalence".

These days, I shoot both APS-C and full frame. For a while, I had to use those calculations in my head to judge which lenses I'd need on each format depending on the use case for any particular shoot. Now, I'm used to each native format and which lenses will work. But that's down to experience.

Why do so many folks get confused by equivalence?


This is an easy one to answer. Amongst those that understand it, there are many views of what "equivalence" means in terms of scope and end results. All of those views are valid, but they don't match up. And then there are well-meaning folks who don't fully understand it, but think they do. That combined group then offers advice - sometimes badly stated, sometimes conflicting - in response to questions asked by those who have little or no understanding of equivalence at all. The recipients may or may not make sense of what's offered, but pass on what parts they think they understand to others. It doesn't take a genius to see how differing opinions and outright mis-information spread.

In summary...


This is where I might expect to get the most push-back, but I'll say it based on what I've read, learned, tried and verified (by some considerable, but not conclusive, experience):

The calculations I mentioned earlier (available at any number of sources) will provide a means of approximating the same field of view and depth of field from a source configuration to a target one - e.g. from full frame to APS-C, medium format to full frame, or large format to medium format.

The optical characteristics of the lens, and the specification / performance of the recording medium (sensor or film) in terms of resolution, dynamic range, noise etc. will potentially have a considerable impact on how the recorded image is rendered - but, field of view and depth of field - at least - should be similar.

TL;DR

If you're shooting an APS-C camera and want similar field of view to full frame, pick a lens with a focal length roughly 1.5 times smaller (e.g. 35mm instead of 50mm). If you want to achieve the same depth of field wide open, that lens needs to offer a maximum aperture 1.5 times wider (e.g. f/1.4 instead of f/2), and preferably wider still to allow for poor optical performance at the fastest apertures. And even if you choose the correct focal length and aperture, don't expect images to look identical between cropped and full frame setups... the lens is the most critical component in the system, and rendering can blow it all apart

Addendum:

I don't expect everyone (or even anyone) to agree with me. But my understanding of equivalence, even if it's flawed, has helped me personally. From that I have to conclude that it might be useful to others, even if some members disagree with it. On that basis, I don't see why we should discount it as confusing or non-productive... if it's explained properly


Last edited by BigMackCam; 01-27-2019 at 02:45 AM.
01-24-2019, 03:26 PM   #2
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I think it is because everything is overthought. Rather than think of lens/ sensor relationship think image circle/ sensor relationship. After all it doesn't matter what camera the lens is on it will always have the same image circle. How the sensor size sits on that circle is what creates the difference and it is easy to visualise once you think this way.
01-24-2019, 03:35 PM   #3
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QuoteOriginally posted by GUB Quote
I think it is because everything is overthought. Rather than think of lens/ sensor relationship think image circle/ sensor relationship. After all it doesn't matter what camera the lens is on it will always have the same image circle. How the sensor size sits on that circle is what creates the difference and it is easy to visualise once you think this way.
Sure... but if we take the lens as a constant and the sensor format as the variable, the various combinations - same lens on full frame, APS-C, m4/3 etc. - would be applicable in different ways and for different use cases, yes? So the concept of equivalence steps in to give us some relationship; i.e. I know that a classic focal length for portraiture is 85mm on full frame... but I don't shoot full frame... instead, I have an Olympus m4/3 camera... so what should I use for portraiture? Well, something around 85 /2 = ~42mm might be a good choice... but if I want shallow depth of field for creative purposes, I'm going to need an awfully fast lens... This is an example where equivalence per se doesn't even matter that much, it's just a case of getting in the very general ball-park... "a fast lens over 40mm on m4/3"...
01-24-2019, 03:42 PM - 1 Like   #4
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But you see this is where you are overthinking it - as an entry level person, it will be the lens you have. But I will say that I was surprised the bokeh smoothness wasn't directly connected to the dof differences between formats. So there is always something to learn!!
K1 bokeh vs K10 apsc bokeh - PentaxForums.com

01-24-2019, 04:03 PM - 1 Like   #5
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QuoteOriginally posted by GUB Quote
But you see this is where you are overthinking it - as an entry level person, it will be the lens you have. But I will say that I was surprised the bokeh smoothness wasn't directly connected to the dof differences between formats. So there is always something to learn!!
K1 bokeh vs K10 apsc bokeh - PentaxForums.com
That's a fair point... but consider the member who has his K-50 and kit lenses, and wants something for portraiture. He's looking at an expensive investment in an FA77 Limited, but may not realise just how much room he needs between the subject and camera in order to take the shots he wants. He asks us if the FA77 is a good choice and we tell him, well, yes - it's a fantastic lens - but actually, since he's using a cropped sensor camera, he'd be better off with a 50mm lens instead, and something faster to offer similar depth of field... unless he has more room to work with...

Similarly (though, perhaps, less common) someone wants a really wide angle lens for landscape work where they want to maximise expression of nearby features... They've read that an ultra-wide 15mm focal length would be useful here, but that's on full frame. Instead, we have to advise them they need something that will give them 10mm or thereabouts.

These aren't uncommon dilemmas for inexperienced users
01-24-2019, 04:31 PM   #6
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Yeah and I have been thinking through these things at the mo.
Upcoming trip to Nepal trekking 10 days.
Maybe charging issues.
Weight issues.
Note I use old glass.
K1 vs K01 so apsc vs FF
AF vs my usual MF (need LV for MF - battery usage)
Zoom vs Prime (only AF prime I have is 40mmxs)
Lens choice -- and this is where the apsc vs FF equivalence thing kicks in but turns out to be reasonably irrelevant.
I am not prepared to carry anything wider than my 28mm because stitching can cover the rest.
50mm is a nobrainer for both formats and if I consign macro capability to a longer lens then a fast 50 does my bokeh world.
Longer needs to be weight constrained and need macro capability. Probably my 135vivitar 2.5 close focusing.
Really the equivalence issues don't come into it.
01-24-2019, 04:33 PM - 1 Like   #7
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QuoteOriginally posted by BigMackCam Quote
but consider the member who has his K-50 and kit lenses
But surely the guy with the K-50 and 18-55mm kit lens will discover that 55mm is a good focal length for portraits in that format by experience? And since he isn't using any other formats, what does it matter which focal lengths work for portraits on those other formats? Would knowing that a 480mm lens on an 8x10 view camera is roughly equivalent be any use to him?*

I apologise for the reductio ad absurdum, but I hope you can see that I'm using it to make a serious point and there is absolutely no sarcasm intended.

*of course you wouldn't actually use a 480mm on the view camera for a portrait anyway because the depth of field would be almost non-existant. Roughly the same field of view though.
01-24-2019, 04:41 PM - 1 Like   #8
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QuoteOriginally posted by Dartmoor Dave Quote
But surely the guy with the K-50 and 18-55mm kit lens will discover that 55mm is a good focal length for portraits in that format by experience? And since he isn't using any other formats, what does it matter which focal lengths work for portraits on those other formats? Would knowing that a 480mm lens on an 8x10 view camera is roughly equivalent be any use to him?*
Indeed... And that would be the ideal scenario. But maybe that same guy came from using a 35mm film camera years ago, and is now confused using his small remaining collection of K-mount lenses (just one example). In any case, many folks will (and do) pose questions regarding lens use pertaining to the particular camera they own. So, whilst I agree wholeheartedly that experience trumps all, when the questions arise, in my opinion it's good to have an explanation rather than telling them, "go out and shoot for six months and make your own mind up" (even though that might be more productive! ).

QuoteOriginally posted by Dartmoor Dave Quote
I apologise for the reductio ad absurdum, but I hope you can see that I'm using it to make a serious point and there is absolutely no sarcasm intended.
No sarcasm ever assumed where you're concerned, Dave I've read too many of your posts and had enough interaction with you to assume anything other than constructive and healthy discussion

01-24-2019, 04:58 PM - 3 Likes   #9
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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.
^^^^THIS!!!!

And the reason even the K-50 owner with the 18-55 might want to know this is if he sees a great portrait taken with an 85 (on FF) or hears some FF camera owner say "50 is too short" for good portraits, he can feel confident that his 55 on APS-C can roughly replicate the field-of-view of the 85. But if he then grows enamored of the "one-eye-in-focus" style of portraiture, then he'll know he's going to need a 55/0.95 on APS-C to replicate the uber-shallow DoF of an 85/1.4 on FF.

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.
01-24-2019, 06:25 PM   #10
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QuoteOriginally posted by BigMackCam Quote
From time-to-time - certainly not infrequently - the subject of "equivalence" comes up in these forums. It's raised for a variety of reasons, often based on significant misunderstanding, e.g. "If I use a 50mm full frame lens on my K-30, is it now a 75mm lens?".

This subject always generates a significant amount of heated conversation, which seems to become more-or-less polarised between two camps - those that think equivalence is a mis-nomer and / or of no practical use, and those who maintain the opposite (with a few folks in the middle ground between).

Indeed, this very discussion once again developed in a recent thread, the original subject of which had nothing to do with equivalence, so I thought I'd start a new thread to discuss this. Those who've heard it all before and want no part of this, please ignore. For the rest, please let me know your thoughts on what follows. Every one of our more experienced members I've spoken to about this has good, valid arguments, and I respect all opinions. I can't promise to agree with them, but if I disagree, it'll be respectful... so I hope each of you will extend the same courtesy to me and others who respond. Sound good?
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.

In 2017 my wife and I spent our vacation in the mountains of West Virginia. We had various tours in mind, but our main reason for being there was to finally ride the "Cass Scenic Railroad" {they use "heritage" steam locomotives to pull tourists up an old logging railroad}. We had skipped this tourist railroad in 1986 (*), so we planned our much-delayed trip up the mountain for a day predicted to have lots of sun. We arrived an hour early, so I was able to look for a good location from which to photograph the train pulling into the station. I noticed a young man with a tablet on a tripod preparing to video the operation, so I stationed myself behind him, partly to stay out of his way and partly because I thought he would add interest to photos of a routine operation. Photos of moving trains are a balancing operation. I chose ISO 400. because that was the highest value I was comfortable using on my K-30 in that setting. Since the train would be moving slowly, I set the shutter speed to 1/250. My camera completed the 'exposure triangle' by selecting an aperture of f/6.7 - which should be enough to put the videographer and the couple-hundred foot train all in the DOF {under weaker light, I would have had to decide which compromise to go with}. As the train came into sight, I continually zoomed my 18-135mm lens, finally taking the photo at what turned out to be 28mm {in cases like this, sometimes I never look to see what the focal length turned out to be}.

Now, suppose I had a K-1 instead - what would have changed? The value of ISO would have depended on what I felt comfortable with from previous use of the camera; I still would have used a shutter speed of 1/250, and again the camera would have selected an aperture to 'complete the triangle' .... I would not have set this, and the value actually set by the K-1 would have depended on what ISO I had set. Assuming I used the FA 28-105mm lens I now have, again I would have zoomed out, and probably taken the photo at 42mm {1.5x28}. The important thing to note is that my choice of ISO depends on my experience with that sensor. People talk about "equivalent ISO value", but since K-30 and K-1 are different generations, there is no reason to believe that my choice would have any relationship to that number {the maximum ISO I was ever willing to use with the K-30 was 800; I've tentatively settled on 12800 for the KP, even though it has the same size sensor as the K-30 does}. I probably would have chosen the same shutter speed {no 'equivalence' there}, and everything else would depend on circumstances. 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.



(*) It turned out that she was 3 weeks pregnant, and her digestive system rebelled at the thought of spending the day on a swaying train. Anything more would be TMI.
01-24-2019, 06:41 PM   #11
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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.
01-24-2019, 06:52 PM   #12
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Equivalence is great with compact cameras. I don't care what my phone lens and sensor size are but know it's 24mm equivalence. Shopping for a Sony cyber-shot? Knowing my choices are 24-70, 24-600, 23-720 but nothing wider any go closer to 20mm? I don't care to know the real size at all. Nikon coolpix b500 who cares what the lens actually is. Its equivalence is 23-900.
01-24-2019, 06:53 PM - 1 Like   #13
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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.

In 2017 my wife and I spent our vacation in the mountains of West Virginia. We had various tours in mind, but our main reason for being there was to finally ride the "Cass Scenic Railroad" {they use "heritage" steam locomotives to pull tourists up an old logging railroad}. We had skipped this tourist railroad in 1986 (*), so we planned our much-delayed trip up the mountain for a day predicted to have lots of sun. We arrived an hour early, so I was able to look for a good location from which to photograph the train pulling into the station. I noticed a young man with a tablet on a tripod preparing to video the operation, so I stationed myself behind him, partly to stay out of his way and partly because I thought he would add interest to photos of a routine operation. Photos of moving trains are a balancing operation. I chose ISO 400. because that was the highest value I was comfortable using on my K-30 in that setting. Since the train would be moving slowly, I set the shutter speed to 1/250. My camera completed the 'exposure triangle' by selecting an aperture of f/6.7 - which should be enough to put the videographer and the couple-hundred foot train all in the DOF {under weaker light, I would have had to decide which compromise to go with}. As the train came into sight, I continually zoomed my 18-135mm lens, finally taking the photo at what turned out to be 28mm {in cases like this, sometimes I never look to see what the focal length turned out to be}.

Now, suppose I had a K-1 instead - what would have changed? The value of ISO would have depended on what I felt comfortable with from previous use of the camera; I still would have used a shutter speed of 1/250, and again the camera would have selected an aperture to 'complete the triangle' .... I would not have set this, and the value actually set by the K-1 would have depended on what ISO I had set. Assuming I used the FA 28-105mm lens I now have, again I would have zoomed out, and probably taken the photo at 42mm {1.5x28}. The important thing to note is that my choice of ISO depends on my experience with that sensor. People talk about "equivalent ISO value", but since K-30 and K-1 are different generations, there is no reason to believe that my choice would have any relationship to that number {the maximum ISO I was ever willing to use with the K-30 was 800; I've tentatively settled on 12800 for the KP, even though it has the same size sensor as the K-30 does}. I probably would have chosen the same shutter speed {no 'equivalence' there}, and everything else would depend on circumstances. 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.



(*) It turned out that she was 3 weeks pregnant, and her digestive system rebelled at the thought of spending the day on a swaying train. Anything more would be TMI.
If you happened to use ISO 400 and 1/250 speed speed in both cameras, then the image from K-30 zoomed to 28mm and aperture of f/6.7 would have much deeper DoF in the final print than the K-1 zoomed to 42mm and aperture of f/6.7.

And if you shoot typical overlook landscapes with the wife in the foreground and pick an aperture that gets both her and infinity in focus, you'd also find that the K-1 needs about 1 stop narrower aperture to make it work.

And if you want to get nice bokeh balls from the lights on an out-of-focus background Christmas tree, you find that the balls are bigger with K-1 and 28-105 @ 28 and f/3.5 than the K-30, 18-135 @ 18 and f/3.5.

Sure, you can find this out by trial and error or you can learn about equivalence and know that you'll get shallower DoF with the K-1 or have to use a narrower aperture to get as much in focus as the K-30 gave you.
01-24-2019, 07:24 PM - 1 Like   #14
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QuoteOriginally posted by photoptimist Quote
Sure, you can find this out by trial and error or you can learn about equivalence and know that you'll get shallower DoF with the K-1 or have to use a narrower aperture to get as much in focus as the K-30 gave you.
In that type of photography, in common with 'street photography',
* Measurement is not a thing.
* Calculation is not a thing.
* Trial-and-error is not a thing {only one chance unless you have a 'way back' machine}

Typically you look for a value f/5.6 or higher (*) that satisfies 'exposure triangle' and hope that it works.
That is a major lesson of "f/8 and be there".
Perfectionists don't understand this.

(*) closer to f/11 or so the better
01-24-2019, 07:31 PM   #15
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QuoteOriginally posted by photoptimist Quote
Sure, you can find this out by trial and error or you can learn about equivalence and know that you'll get shallower DoF with the K-1 or have to use a narrower aperture to get as much in focus as the K-30 gave you.
Or you can just learn an FF is one stop shallower DoF than the same lens on APS-c. (And not learn equivalence.)

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.
As I said, IMHO, equivalence is make a work project.
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