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I know that explanation, it only explains, why larger sensors produce less noise giving cleaner images (that's why people buy them). You try to convince me, that larger sensors because of larger photosites records more light then it is there ? Maybe they have this ability, but shouldn't they keep ISO standards ? What you are saying ISO 100 on FF sensor equals ISO ... 250 on APS sensor ?Can you explain it a bit better ? If there is the same intensity of light per every square millimetre of the sensor how comes bigger sensor should sense more light ?
Well I can.. problem is doing so in such a fashion that the post doesn't become longer than Tolstoy's War and Peace.. lol. Ok, I'll give it a quick stab, and no this is by no means complete but hopefully it will cover the basics.
A sensor in a digital camera has millions of spots that are sensetive to light, called photosites. Each photosite records information about what is being "seen" through the lens, so the more photosites you have and the larger they are naturally the more information that is being collected. A larger sensor allows for larger photosites - and a larger photosite will collect more from a ray of light than a smaller one can. If it helps think of it in terms of water. If you put a coffee cup on the floor and pour water into it, once the cup is full any more water will flow out of the top and simply be wasted. Replace the cup with a bucket, and now you can pour the same amount of water and because of the buckets larger size, it will collect a lot more of the water.
The amount of water your pouring doesn't change (much like the amount of light coming into the camera doesn't change when your using the same aperture) however because you now have row after row of buckets instead of row after row of coffee cups, the amount of "water" or in this case the amount of information from the light captured that is retained is a whole lot more.
What I am saying is that the larger photosites on a full frame sensor will capture more information when exposed to the same amount of light than the smaller photosites of an APS-C sensor, and as a result you will have better dynamic range and less noise at the same aperture settings on a full frame sensor as you will on a APS-C sensor when the two are exposed to the exact same amount of light.
If you'd like you can translate that into an ISO equivalent or an Fstop equivalent to describe how the full frame sensor is more efficient and captures more information using the same amount of light than it's smaller APS-C cousin, if you prefer to think of it in those terms of you certainly can. The thing to note here is that at the same aperture and the same ISO setting and shutter speed the Full Frame is going to have a lot more information to work with to create the final image, which is going to result in a lot less noise and much better dynamic range. Using the exact same settings on an APS-C will result in a lot more noise, so the net result is that the full frame is going to give you much better results in low light conditions.