ASPC vs 1 inch sensor and low light abilities (aperture)

FWIW, equivalence is a poorer explanation than the explanation without equivalence, IMHO.
Equivalence in 10 bullets:

Neither the focal length nor the f-ratio of a lens change as a function of sensor (for example, a 50mm f/1.4 lens is a 50mm f/1.4 lens, regardless of the sensor behind the lens). However, the effect of both the focal length and the relative aperture (f-ratio) on the visual properties of the photo very much depend on the sensor, and scale in direct proportion to the size of the sensor.

In short, 25mm f/1.4 on mFT (4/3) is equivalent to 50mm f/2.8 on FF (FX), where "equivalent to" means:
  • The photos all have the same diagonal angle of view (25mm x 2 = 50mm) and aperture diameter 25mm / 1.4 = 50mm / 2.8 = 18mm).
  • The photos all have the same perspective when taken from the same position.
  • The photos all have the same DOF (as well as diffraction softening) when they are taken from the same position with the same focal point and have the same display size.
  • The photos all have the same motion blur for the same exposure time (regardless of pixel count).
  • The same total amount of light falls on the sensor for the same scene, DOF, exposure time, lens transmission (e.g. if the 25mm lens is t/1.6 at f/1.4 and the 50mm lens is t/3.2 at f/2.8), and vignetting.
  • The same total light falling on the larger sensor will result in a lower exposure than the smaller sensor (the same total light over a larger area results in a lower density of light on the sensor).
  • The larger sensor system will use a concomitantly higher ISO setting for a given brightness on the LCD playback and/or for the OOC (out-of-the-camera) jpg due to the lower exposure (keeping in mind that the ISO setting affects noise only inasmuch as higher ISO settings result in less electronic noise than lower ISO settings -- e.g. a photo "properly exposed" at f/2.8 1/100 ISO 1600 will have less noise than a photo of the same scene at f/2.8 1/100 ISO 200 pushed to the same brightness).
  • The same total light will result in the same noise if the sensors record the same proportion of light falling on them (same QE) and add in the same electronic noise, regardless of pixel count and ISO setting, keeping in mind that the electronic noise matters only for the portions of the photo made with very little light.
  • If the 25mm lens at f/1.4 is twice as sharp (lp/mm) as the 50mm lens at f/2.8, the sensors have the same number of pixels, and the AA filter introduces the same blur, then all systems will also resolve the same detail (lw/ph).
  • Other elements of IQ, such as bokeh, color, distortion, etc., as well as elements of operation, such as AF speed/accuracy, size, weight, etc., are not covered in this use of the term "equivalent".
Now your turn to post your superior explanation not making use of Equivalence.
I realize you love that stuff but the disagreement is this:

You think changing ISO setting makes lens equivalent; I think because you need to change the ISO setting, lens are not equivalent.
Because you cannot get the incorrect notion out of your system that noise is a function of ISO setting and that the same ISO on differently-sized sensors results in a similar amount of noise. ISO 100 on m43 results in a vastly different amount of noise than ISO 100 on FF would. The question is really why you would not change ISO when changing sensor sizes? You change focal lengths when you change sensor sizes, why would you also not change the ISO setting? Changing the focal length (when changing sensor size) allows you to keep the AOV constant, changing the ISO setting allows you to keep the shot noise constant.
 
Such as "the image projected at the focal plane" would be rather ephemeral without the sensors, however. ;-)
And AOV of a lens is also largely ephemeral without defining a sensor size. Sure, the lens projects an AOV limited by its image circle but as you say, without a sensor capturing it, that is rather ephemeral.
 
I keep seeing this claim, and it puzzles me, because those of of us who used different film formats always had to deal with conversions to determine equivalence among formats, often as part of decision making about which to use; sometimes just as a check on knowledge of our craft. It wasn't called "equivalence" or use "crop factor" in those days, but the science and fundamental principles are the same. One thing that was different, and which can be handled much more neatly with digital photography, is inclusion of the ISO factor. Because the choices of film ISO range were more limited and the effects of changing ISO not a predictable as we have now, we tended to ignore it (assume it was the same) when comparing formats. This tended to limit the flexibility of using larger formats; to achieve the depth of field of a smaller format we had to use f/64, and with limited ability to increase ISO, just accept the need to increase shutter time.

Anyway, equivalence isn't a new concept, through it has been more formalized for digital. Those who decry its applicability and usefulness (even if that isn't every day) are simply choosing to ignore one of the more fascinating aspects of their craft.
What is different is also that noise in images scales much better with total light on modern digital sensors than it ever did on film. An ISO 25 film on 135-mm was not quite equivalent to ISO 100 film on 6x7 MF (ISO 100 on 6x7 MF was better).
 
What about the shutter-speeds if the APS was shot @ f/3.5 and the 1" also @ f/3.5 ??? (with same ISO)
What is your fixation with shooting differently-sized sensors at the same ISO? What is that supposed to achieve? In fact, why would you ever shoot differently-sized sensors at the same ISO (when shooting the same subject)?
When using a bright prime on the larger sensor camera while being shutter time limited and DOF doesn't matter.

So an apples to oranges situation where any proper ILC will outwit any 1 inch camera.

I would never shoot the Rx100 mk 3 at F3.5 in order ro criple it compared to a a6000 with the 16-50mm garbage kit.

I would shoot both wide open and then the Rx100 would have a negligible advantage.

That said i shoot Fuji and therefore have access to a better faster kit lens. Which has a small advantage at the wide-end to a substantial advantage at the long end.

But those advantages do come at a substantial increase in both size and weight.
 
The point is Your Equivalence is not new...
Not at all. Just the term and the application to digital photography.
...nor does it make apertures equivalent.
It results in the same aperture diameter and equivalent relative apertures.
You are calling what he taught 15years ago "Equivalence" and photography is way older than 15 years...
But the principles are the same as ever.
I realize "Equivalence" is your child but I'm afraid it's an adopted child - of course, nothing wrong with adopted children...
There is, however, quite a bit wrong with willful ignorance.
So why are the sensors not equivalent?
Equivalent photos are defined as photos with the same perspective, framing, DOF / diffraction / total light on sensor, exposure time, brightness, and display size. Equivalent lenses are defined as lenses with the same angle of view and aperture diameter.
Indeed, you get to define it and then you need to sell it - some of us see no need to buy it.
If something does not cost any money, then how is it being sold?
So, how will you define "equivalent sensors" in a manner that is consistent with the above?
Actually, you have mistaken the sensor equivalence to the lens equivalence. For example the angle of view is determined by FL and the sensor size. The lens' angle of view does not change. What you are saying is that the difference in sensor size can be equalized to result in equivalent photos.
The focal length of the lens combined with the size of the sensor determines the angle of view, yes.
But explaining in terms of lens equivalence is the fault.
The diameter of the lens aperture determines the DOF for a given perspective and framing, and also determines the total amount of light falling on the sensor for a given exposure time.
It's no more precise than some folks thinking Mirror-less is equivalent to DLSR and some folks thinking those are not.
Non sequitur.
What is there not to see that "Equivalence" is rather subjective conclusion.

OK, how about this -

You think changing ISO setting makes lens equivalent; I think because you need to change the ISO setting, lens are not equivalent.
Would you object less if he had chosen some other word, like 'parity'? If so, just substitute the word of your choice each time you read 'equivalence'. Then you can stop belly-aching about it.
 
But the OP did not even seem concerned with "DOF" ... the question was simply "capability".

And the answer was simple ... f/1.8 has more "capability" than f/3.5 .... period (ignoring sensor-size and resulting noise and DOF differences)
Really? A f/2.4 smartphone camera has more capability than a f/3.5 APS-C lens? Only if with capability you mean being able to fit the camera into your pocket.
 
Yes .. the total light is less ... BUT ... it is concentrated on a SMALLER sensor for the amount/area is the SAME.
Sure, but light amount per area is not what determines noise. Light per area actually has very little effect on IQ. So why would it matter that it is the same? What would it matter for car performance if two car engines have the same amount of power per engine displacement?

The ISO setting (which defines what light per area and time turns into final image brightness) is not what determines noise. Total light determines noise and total light is sensor size divided by ISO.
Not quite -

Regardless of the total light, the image noise is the same when a crop sensor image is compared to the crop image of the FF sensor. The cropped image from a FF sensor is not less noisy because it came from more total light.

The above is obvious if one think of the crop mode of a FF camera image and cropped image of the said FF camera.
Yeah, and cropping from a FF sensor still uses the total light the complete FF sensor received. Not. So what again was your point?
He's confusing himself as always, partly because of not saying what he means clearly. He believes that some how cropping the FF sensor does not affect the 'total light' from which the image is made, because he sees 'total light' as a sensor property, not an image one.
 
The point is Your Equivalence is not new...
Not at all. Just the term and the application to digital photography.
...nor does it make apertures equivalent.
It results in the same aperture diameter and equivalent relative apertures.
You are calling what he taught 15years ago "Equivalence" and photography is way older than 15 years...
But the principles are the same as ever.
I realize "Equivalence" is your child but I'm afraid it's an adopted child - of course, nothing wrong with adopted children...
There is, however, quite a bit wrong with willful ignorance.
So why are the sensors not equivalent?
Equivalent photos are defined as photos with the same perspective, framing, DOF / diffraction / total light on sensor, exposure time, brightness, and display size. Equivalent lenses are defined as lenses with the same angle of view and aperture diameter.
Indeed, you get to define it and then you need to sell it - some of us see no need to buy it.
If something does not cost any money, then how is it being sold?
So, how will you define "equivalent sensors" in a manner that is consistent with the above?
Actually, you have mistaken the sensor equivalence to the lens equivalence. For example the angle of view is determined by FL and the sensor size. The lens' angle of view does not change. What you are saying is that the difference in sensor size can be equalized to result in equivalent photos.
The focal length of the lens combined with the size of the sensor determines the angle of view, yes.
But explaining in terms of lens equivalence is the fault.
The diameter of the lens aperture determines the DOF for a given perspective and framing, and also determines the total amount of light falling on the sensor for a given exposure time.
It's no more precise than some folks thinking Mirror-less is equivalent to DLSR and some folks thinking those are not.
Non sequitur.
What is there not to see that "Equivalence" is rather subjective conclusion.

OK, how about this -

You think changing ISO setting makes lens equivalent; I think because you need to change the ISO setting, lens are not equivalent.
Why? Because any given ISO values infers certain IQ properties to the photo taken? Of course, most of the discussion only applies in light (and thus shutter speed) limited situations (unless the smaller sensor has a correspondingly lower base ISO).

Why would two images, shot with two cameras with differently-sized sensors where the ISO was adjusted such that both images received the same total amount of light, not be equivalent if they had the same AOV, DOF and noise? Is the ISO setting a parameter that is visible in the final image beyond its effect on noise?
 
They are making this way more complicated than it needs to be.

Just remember that "equivalence" ONLY applies to DOF, (not exposure "settings").
Joe, most folks here apply "equivalence" primarily to focal length. :-0
Equivalence, what a wonderful word :-P

It suggests to the innocents that one can get more for less ;-)
I suggest you look up the word 'equivalence' in a dictionary if you are not sure of its meaning. An example usage of the word from outside photography would be for example that an equivalent amount of currency would buy you the same goods or services in two different countries.
 
Check out this article, it shows why different setting were used for different size sensors to get similar photos. From personal experience I can tell you in studio I use different ISO, shutter speeds and apeture between my Nikon d810 and my mamiya leaf credo 50.


They post a photo of a Nikon shot and iPhone shot one at f2.2 and one at f16 with different ISO and shutter speeds to get a similar photo than explain why.
 
They are making this way more complicated than it needs to be.

Just remember that "equivalence" ONLY applies to DOF, (not exposure "settings").
Joe, most folks here apply "equivalence" primarily to focal length. :-0
Equivalence, what a wonderful word :-P

It suggests to the innocents that one can get more for less ;-)
I suggest you look up the word 'equivalence' in a dictionary if you are not sure of its meaning. An example usage of the word from outside photography would be for example that an equivalent amount of currency would buy you the same goods or services in two different countries.
and with his little quip 'it suggests to the innocents that one can get more for less ;-)' he has exactly reversed the situation. The people who think they are getting 'more for less' are the ones who think that by using a smaller sensor, they are getting a smaller, cheaper system with more depth of field that gives them no hit anywhere else. That's why they don't like equivalence, it quantifies rather precisely the hit they are actually taking. Many of those people also seem to believe that lack of equivalence stops with their preferred format - everything smaller indeed does take the hit.
 
I appreciate your removal of the term "Marketing Socket Heads" and your replacement of it by "Marketing Slot Heads". It means a lot to me, even if no one else in the whole world cares.

Actually, it doesn't mean a lot to me. But thanks anyway.
Well, it didn't mean a lot to me either. That's why I didn't struggle w/ the change. Anything for my friends. ;-)

 
I keep seeing this claim, and it puzzles me, because those of of us who used different film formats always had to deal with conversions to determine equivalence among formats, often as part of decision making about which to use; sometimes just as a check on knowledge of our craft. It wasn't called "equivalence" or use "crop factor" in those days, but the science and fundamental principles are the same. One thing that was different, and which can be handled much more neatly with digital photography, is inclusion of the ISO factor. Because the choices of film ISO range were more limited and the effects of changing ISO not a predictable as we have now, we tended to ignore it (assume it was the same) when comparing formats. This tended to limit the flexibility of using larger formats; to achieve the depth of field of a smaller format we had to use f/64, and with limited ability to increase ISO, just accept the need to increase shutter time.

Anyway, equivalence isn't a new concept, through it has been more formalized for digital. Those who decry its applicability and usefulness (even if that isn't every day) are simply choosing to ignore one of the more fascinating aspects of their craft.
What is different is also that noise in images scales much better with total light on modern digital sensors than it ever did on film. An ISO 25 film on 135-mm was not quite equivalent to ISO 100 film on 6x7 MF (ISO 100 on 6x7 MF was better).
Agreed; I mentioned that above. Though at the time I don't think I was as cognizant of the reasons, it was pretty well accepted that there wasn't much you could do with ISO; there were only a few consumer films available with somewhat higher ISO ratings, and they inevitably involved a trade-off in grain and latitude. And pushing in development definitely did not produce equivalent images. I shot 4 x 5 and was acutely aware that if i wanted the DoF I could get with 35 mm, I had to choose subjects that worked with a longer shutter time.

Dave
 
Check out this article, it shows why different setting were used for different size sensors to get similar photos. From personal experience I can tell you in studio I use different ISO, shutter speeds and apeture between my Nikon d810 and my mamiya leaf credo 50.

https://photographylife.com/sensor-size-perspective-and-depth-of-field

They post a photo of a Nikon shot and iPhone shot one at f2.2 and one at f16 with different ISO and shutter speeds to get a similar photo than explain why.
A great example of the lengths some people will go to to avoid admitting they were wrong.

In this article, linked at the top of the one you put forward:


Nasim Masurov did his best to rubbish equivalence. A bit of a strange article, in fact, because he starts off reproducing every result of equivalence, then he chokes on his need to declare that 'smaller format lenses have exactly the same light gathering capabilities as larger format lenses at the same f-stop, for their native sensor sizes'. Of course it's nonsense, but having got that one wrong, he has to mangle everything else subsequently so as not to be wrong. So then they try to re-write 'Equivalence' (deftly substituting the word 'effective' for 'equivalent') reproducing all the results apart from noise equivalence, which must be discounted because Mr Masurov has declared that shot noise does not depend on 'total light'.
 
The point is Your Equivalence is not new...
Not at all. Just the term and the application to digital photography.
...nor does it make apertures equivalent.
It results in the same aperture diameter and equivalent relative apertures.
You are calling what he taught 15years ago "Equivalence" and photography is way older than 15 years...
But the principles are the same as ever.
I realize "Equivalence" is your child but I'm afraid it's an adopted child - of course, nothing wrong with adopted children...
There is, however, quite a bit wrong with willful ignorance.
So why are the sensors not equivalent?
Equivalent photos are defined as photos with the same perspective, framing, DOF / diffraction / total light on sensor, exposure time, brightness, and display size. Equivalent lenses are defined as lenses with the same angle of view and aperture diameter.
Indeed, you get to define it and then you need to sell it - some of us see no need to buy it.
If something does not cost any money, then how is it being sold?
So, how will you define "equivalent sensors" in a manner that is consistent with the above?
Actually, you have mistaken the sensor equivalence to the lens equivalence. For example the angle of view is determined by FL and the sensor size. The lens' angle of view does not change. What you are saying is that the difference in sensor size can be equalized to result in equivalent photos.
The focal length of the lens combined with the size of the sensor determines the angle of view, yes.
But explaining in terms of lens equivalence is the fault.
The diameter of the lens aperture determines the DOF for a given perspective and framing, and also determines the total amount of light falling on the sensor for a given exposure time.
It's no more precise than some folks thinking Mirror-less is equivalent to DLSR and some folks thinking those are not.
Non sequitur.
What is there not to see that "Equivalence" is rather subjective conclusion.

OK, how about this -

You think changing ISO setting makes lens equivalent; I think because you need to change the ISO setting, lens are not equivalent.
Would you object less if he had chosen some other word, like 'parity'? If so, just substitute the word of your choice each time you read 'equivalence'. Then you can stop belly-aching about it.
I'm not belly-aching about what word I would use; it's the word that DPR uses that I'm belly-aching about.
--
Bob.
“The picture is good or not from the moment it was caught in the camera.”
Henri Cartier-Bresson.
 
The point is Your Equivalence is not new...
Not at all. Just the term and the application to digital photography.
...nor does it make apertures equivalent.
It results in the same aperture diameter and equivalent relative apertures.
You are calling what he taught 15years ago "Equivalence" and photography is way older than 15 years...
But the principles are the same as ever.
I realize "Equivalence" is your child but I'm afraid it's an adopted child - of course, nothing wrong with adopted children...
There is, however, quite a bit wrong with willful ignorance.
So why are the sensors not equivalent?
Equivalent photos are defined as photos with the same perspective, framing, DOF / diffraction / total light on sensor, exposure time, brightness, and display size. Equivalent lenses are defined as lenses with the same angle of view and aperture diameter.
Indeed, you get to define it and then you need to sell it - some of us see no need to buy it.
If something does not cost any money, then how is it being sold?
So, how will you define "equivalent sensors" in a manner that is consistent with the above?
Actually, you have mistaken the sensor equivalence to the lens equivalence. For example the angle of view is determined by FL and the sensor size. The lens' angle of view does not change. What you are saying is that the difference in sensor size can be equalized to result in equivalent photos.
The focal length of the lens combined with the size of the sensor determines the angle of view, yes.
But explaining in terms of lens equivalence is the fault.
The diameter of the lens aperture determines the DOF for a given perspective and framing, and also determines the total amount of light falling on the sensor for a given exposure time.
It's no more precise than some folks thinking Mirror-less is equivalent to DLSR and some folks thinking those are not.
Non sequitur.
What is there not to see that "Equivalence" is rather subjective conclusion.

OK, how about this -

You think changing ISO setting makes lens equivalent; I think because you need to change the ISO setting, lens are not equivalent.
Would you object less if he had chosen some other word, like 'parity'? If so, just substitute the word of your choice each time you read 'equivalence'. Then you can stop belly-aching about it.
I'm not belly-aching about what word I would use; it's the word that DPR uses that I'm belly-aching about.
I knew that. That's why I suggested that you mentally substitute whatever word you'd like to use instead and stop the belly-aching, which isn't getting anyone anywhere, and hasn't for a very long time.
 
The point is Your Equivalence is not new...
Not at all. Just the term and the application to digital photography.
...nor does it make apertures equivalent.
It results in the same aperture diameter and equivalent relative apertures.
You are calling what he taught 15years ago "Equivalence" and photography is way older than 15 years...
But the principles are the same as ever.
I realize "Equivalence" is your child but I'm afraid it's an adopted child - of course, nothing wrong with adopted children...
There is, however, quite a bit wrong with willful ignorance.
So why are the sensors not equivalent?
Equivalent photos are defined as photos with the same perspective, framing, DOF / diffraction / total light on sensor, exposure time, brightness, and display size. Equivalent lenses are defined as lenses with the same angle of view and aperture diameter.
Indeed, you get to define it and then you need to sell it - some of us see no need to buy it.
If something does not cost any money, then how is it being sold?
So, how will you define "equivalent sensors" in a manner that is consistent with the above?
Actually, you have mistaken the sensor equivalence to the lens equivalence. For example the angle of view is determined by FL and the sensor size. The lens' angle of view does not change. What you are saying is that the difference in sensor size can be equalized to result in equivalent photos.
The focal length of the lens combined with the size of the sensor determines the angle of view, yes.
But explaining in terms of lens equivalence is the fault.
The diameter of the lens aperture determines the DOF for a given perspective and framing, and also determines the total amount of light falling on the sensor for a given exposure time.
It's no more precise than some folks thinking Mirror-less is equivalent to DLSR and some folks thinking those are not.
Non sequitur.
What is there not to see that "Equivalence" is rather subjective conclusion.

OK, how about this -

You think changing ISO setting makes lens equivalent; I think because you need to change the ISO setting, lens are not equivalent.
Why? Because any given ISO values infers certain IQ properties to the photo taken?
No, because one ends up thinking that a crop of a larger sensor image is less noisy than the same image from a crop sensor.
Of course, most of the discussion only applies in light (and thus shutter speed) limited situations (unless the smaller sensor has a correspondingly lower base ISO).

Why would two images, shot with two cameras with differently-sized sensors where the ISO was adjusted such that both images received the same total amount of light, not be equivalent if they had the same AOV, DOF and noise? Is the ISO setting a parameter that is visible in the final image beyond its effect on noise?
 
They are making this way more complicated than it needs to be.

Just remember that "equivalence" ONLY applies to DOF, (not exposure "settings").
Joe, most folks here apply "equivalence" primarily to focal length. :-0
Equivalence, what a wonderful word :-P

It suggests to the innocents that one can get more for less ;-)
I suggest you look up the word 'equivalence' in a dictionary if you are not sure of its meaning. An example usage of the word from outside photography would be for example that an equivalent amount of currency would buy you the same goods or services in two different countries.
What if a dollar beer cost 1000 pesos but 5 dollar whisky cost 10,000 pesos? ;-)

If you put 50mm f/2 lens on a 4/3 camera and the AOV now looks like of 100mm and brightness now looked like f/4 of FF cam, I'll say yea, OK, 50mm f/2 is equivalent to 100mm f/4; but that's not the case, is it?

Personally, I would simply say the 4/3 image is equivalent to a cropped FF image. Rest will kinda fall in...
 
What is there not to see that "Equivalence" is rather subjective conclusion.

OK, how about this -

You think changing ISO setting makes lens equivalent; I think because you need to change the ISO setting, lens are not equivalent.
Why? Because any given ISO values infers certain IQ properties to the photo taken?
No, because one ends up thinking that a crop of a larger sensor image is less noisy than the same image from a crop sensor.
Why would one think that? Nothing said here would imply anything like this. Coupling a lens with a sensor that is smaller than the lenses image circle or taking a crop from a sensor (who is fully covered by the lens) results in the same reduced equivalent f-stop as using smaller-sensored camera with a matched lens.

Total light collected is the effectively used sensor area times the actual f-stop. And equivalent f-stop (like equivalent focal length) is the f-stop that produces the same image (using the same total light collected) as a lens+sensor combination of the reference sensor size (which has almost always 24 x 36 mm) would.
 
Equivalence, what a wonderful word :-P

It suggests to the innocents that one can get more for less ;-)
I suggest you look up the word 'equivalence' in a dictionary if you are not sure of its meaning. An example usage of the word from outside photography would be for example that an equivalent amount of currency would buy you the same goods or services in two different countries.
What if a dollar beer cost 1000 pesos but 5 dollar whisky cost 10,000 pesos? ;-)
That problem doesn't exist with equivalent f-stops and focal length since the same factor applies for AOV (ie, the crop factor applied to focal length), DOF (ie, the crop factor applied to f-stop) and total light (ie, the crop factor applied to f-stop) and thus shot noise. And, in a calculated attempt to make your head explode, could also be extended to 'equivalent ISO' (though you'd need to square the crop factor for that).
If you put 50mm f/2 lens on a 4/3 camera and the AOV now looks like of 100mm and brightness now looked like f/4 of FF cam, I'll say yea, OK, 50mm f/2 is equivalent to 100mm f/4; but that's not the case, is it?
The brightness inside the camera is not the same but why do you care about the brightness inside the camera? You only care about noise in the recorded image, and that is the same in a m43 50 mm f/2 image as in a FF 100 mm f/4 image.

I'd suggest that you repeat after me:

"Noise is a function of the total light collected and not of the brightness of the projected image at the sensor, where total light is brightness times effectively used sensor area (and exposure time naturally)."

Because if you don't do so, I have to conclude that I am essentially talking to a brick wall.
Personally, I would simply say the 4/3 image is equivalent to a cropped FF image. Rest will kinda fall in...
If you crop a 50 mm f/2 FF image to 4/3 size, you get exactly the same thing as taking a 50 mm f/2 m43. Same as if you take a 10 x 15 cm piece of paper and compare it with the result of cutting down an A4-sized paper to 10 x 15 cm. The two piece of paper will end up weighing the same.
 
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