Originally posted by falconeye 1. Please, get the part about crop factors right. Ken did make no mistake in computing 55/43=1.27 as the rations of diagonals of 645D vs 35mm. Also, crop factors are >1 by definition as being relative to a mount's full image diagonal (i.e., not 0.8). If you must compare to 35mm, call it conversion factor instead.

Ken Rockwell based his sensor comparison on his faulty mathematics.

Comparing diagonals only makes sense when the rectangles in question have the same aspect ratio. i.e. it only makes sense compare diagonals of a 3:2 sensor vs another 3:2 sensor, a 4:3 sensor vs another 4:3 sensor, a 4:3 monitor vs another 4:3 monitor, a 16:9 LCD vs another 16:9 plasma, etc.

It is because when we compare the ratio between linear dimensions, the ratio between the areas is guaranteed to be the square thereof - and when we compare sensor sizes, the fundamental measurement is between area - comparing linearly is only a convenient measure.

16x24 = 384, sqrt(16x16+24x24) ~ 28.8

24x36 = 864, sqrt(24x24+36x36) ~ 43.3

864/384 = 2.25 ~ (43.3/28.8)x(43.3/28.8)

In fact, we don't even need to calculate the areas or even the diagonals to see an FF sensor is 2.25 times the area of an APS-C sensor, because we can measure one side of each sensor and square the quotient: (24/16)*(24/16) = 2.25.

However, this guarantee falls apart the moment we start to compare linear dimensions between shapes that aren't similar, e.g. rectangles with different aspect ratio.

To illustrate this point, imagine someone makes a sensor of size 1mm x 100mm. Its diagonal length is about 100mm (more than double the FF sensor diagonal!!) but its area is only 100mm squared (only a quarter of APS-C sensor area!!)

If you say my example is too imaginary and that nobody will ever make a 1mm x 100mm sensor, how about if somebody makes a 16:9 sensor with size 39mm x 22mm. Now its diagonal is 44.8 mm, slightly but clearly longer than FF's diagonal. However, its area is now 858 mm squared, also slightly but clearly smaller than FF's area.

So in terms of area, the meaningful measurement of light-collecting ability, this 16:9 sensor is smaller than an FF sensor, but with Ken-Rockwell-Logic (TM), it would seem that the 16:9 sensor is larger than an FF sensor.

Demonstrably, Ken either does not know enough photography to understand the photographic reason behind linear dimension comparisons, or maybe he understands, but screwed up his calculations with his sorry high-school-failing mathematics.

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Last edited by wolfier; 03-23-2010 at 08:36 AM.
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