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And this in practical (and very simplistic) terms can be demonstrated by camera phones in low light. Lots of megapixels on a tiny sensor = noisy images.OK, let's see if we can disentangle this a bit.
Firstly, other things being equal, smaller pixels mean there is more noise at the pixel level. So for example consider the 50D and the 5D II. These came out at the same time so presumably they have sensors which use similar technology. The 50D has 15 MP and the 5D II has 20 MP, but if you scaled up the 50D sensor to full frame size it would have about 38 MP. Therefore the pixels on the 50D are smaller, and you would expect the noise to be worse.
(You have to be very careful when making comparisons like this though, because sensor technology has been improving so rapidly. The "other things being equal" means you have to compare sensors made by the same company at the same time if you want to be confident in your conclusion.)
Secondly, other things being equal, a newer sensor will tend to have less noise at the pixel level than an older one. That's just your basic technology improvement. (Note that it's the age of the sensor design that matters, not the age of the camera. Sometimes Canon will bring out a new camera using the same sensor as its predecessor, and sometimes they cascade down older sensors into the lower models.)
But the third effect is the one I mentioned earlier; reducing the image size reduces noise. If you're aiming for a constant output size such as 2 MP for onscreen viewing or 8 MP for a print, then down sampling from a higher MP image will reduce the noise more than down sampling from a lower MP image.
Does that make sense?
Putting it all together: you'd expect a 50D to have less noise at the pixel level than a 40D because it's a newer sensor design, and if Canon had left it at 10 MP then it surely would have. But they increased the pixel count by 50%, and smaller pixels are noisier, and the net effect was no significant difference at the pixel level. There's still an advantage to the 50D when you're reducing the image size for display or print, but it's probably not a very big advantage.
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