Unfortunately, that's not the case for some complicated science. I'll try and explain it. The crucial thing to understand first is that the noise caused by low light (not the electronics) is proportional only to the number of photons hitting the image (statistically the S/N varies as sqrt of N). Accordingly, the number of photons per duck, which determines the signal to noise of the image due to light, does not depend on the f-stop - it depends just on the diameter of the front element of the lens (technically the entrance pupil). The amount of light let into the lens is the area of the front element times the light intensity times the shutter speed. Put a 2xTC on a telephoto lens, you double the f-number and lower the intensity of light hitting the sensor by a factor of 4, so the image of the duck has 1/4 of the number of photons hitting it. But, the area of the duck increases by a factor of 4 so the total number of photons hitting the duck remains unchanged. So, if you simply double the iso when the 2x TC is on, you can use the same shutter speed as without it, and end up with the same S/N. If you do the opposite and put a 2x focal reducer on the MFT, you do indeed increase the light intensity hitting the duck by a factor of 4 but you reduce the area of the duck by a factor of 4 and so the same number of photons hit the duck.The way I see it is that an MFT camera can use a focal reducer with every EF lens as a full-frame camera while gaining a stop of light while a full-frame camera can use a 2x teleconverter with a limited number telephoto lenses while losing two stops of light.
While an MFT camera with a focal reducer can't beat a full-frame camera it is better at being a full-frame camera than a full-frame camera with a 2x teleconverter is at being an MFT camera.
Of course, we can split the difference by going APS-C
#R7
Another way of looking at it, which is less technical, is if you have a smaller image you have to enlarge it more than you have to enlarge a larger image to view them both at the same size.
We use f-numbers to determine exposure, but it's the diameter of the lens that is the crucial factor in how good the image is. And this is true for most things about the image. For example, although it seems counterintuitive, if you had an incredibly high resolution sensor it would be the just the diffraction limits that determine resolution and you wouldn't need long telephoto lenses. This is because diffraction is determined by the lens diameter. It's only because our sensors are still of low resolution that increasing focal length is important.
Although it has been suggested the science isn't important, it is useful when choosing and considering lenses. For example, the RF 100-500mm f/7.1 has the same size front element as the 100-400mm II f/5.6 and so the f/7.1 lens lets in the same amount of light and it's no disadvantage to raise the iso to compensate for this. The same is true of the 800mm f/11, which can be used at twice the iso of the 400mm f/5.6 without increasing the noise in a cropped image of a duck. I did some threads about this.
Extenders and high iso with the R5
Concerns are frequently expressed about lenses like the RF 100-500mm with f/7.1 being narrow and so the images must surely be noisy because high isos are necessary in dim light? Some claim the 400mm f/5.6 is superior in low light because it is 2/3 of a stop faster (or a 1/3rd faster than the...
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Iso, noise, extenders, cropping, and 600mm f/6.3 vs 500mm f/5.6 zooms
Another one of my geek notes that may be of some practical use. This has been stimulated by discussion in the threads about 600mm f/6.3 vs 500mm f/5.6 telephoto lenses. It is usually thought that the larger f-number of the longer lens means either a slower shutter speed or introducing more...
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Effects of diffraction and R5/R6 sensor on resolution of f/5.6, f/7.1 and f/11 lenses and TCs
Another of my geek articles, which does have some implications for actual use. What I do here is to calculate the contributions of diffraction and sensor Mpx size (R5 vs R6) to the resolving power of the 400mm f/5.6 and 500mm f/7.1 zooms and the 600mm and 800mm f/11 primes and how resolution is...
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