Started Jul 9, 2013 | Questions thread
Re: Triangle explanation

Press Correspondent wrote:

If I understand your question, it is about a graphical representation of the exposure values. You started with 3 values and therefore assumed a triangle. This assumption was the root of the problem of getting the correct answer. Then several users suggested the 4th parameter, the available light. It was a great insight, just not presented in the quantitative form. Finally, Jeff presented a formula, except reversed and unnecessarily overcomplicated. So let's get all this straight

The way I understand your question, it is about photographic CONTROLS, of which you started with the common 3. The 4th CONTROL is the amount of light. You can control it in a studio by the power of your lamps, but most commonly this is done by the automatic flash duration. Fir example, if you set your camera in a manual mode, but shoot with flash, the exposure is not set manually. It is still set automatically by the duration of the flash. Therefore in this example you can freely change all 3 of your common controls and still have the proper exposure. This has nothing to do with the amount of available light that you cannot CONTROL. Interestingly, one poster even mentioned a tesseract, which would represent the frame of reference for this case. However, for simplicity, let's stick to your original question and forget about the 4th control. This is the formula given by Jeff:

"Let S be ISO, t be shutter duration, N be f-Number. We'll call image brightness B where

B = log2(N^2/t) - log2(S)"

Well, actually the image brightness is proportional to the shutter duration, not reverse proportional. The same goes for ISO: the higher the ISO value, the brighter the output image is, nit vice versa. I am sure Jeff understands all this and these are not errors, but using a different convention. So let's simplify it.

Let A be the aperture control or the f-Number squared: A = N^2

Let T be the actual shutter duration (not the reversed one): T = 1/t (e.g. 0.03 sec = 1/30 sec)

Let S be sensitivity measured in the ISO numbers, such as 100, 1600, etc.

Then our brightness CONTROL number is:

B = A*T*S

Simple enough, now, where is the triangle here? Imagine 3 axes, X, Y, Z, just like in 3D graphs. They form a triangular pyramid of sort. This is as far as we can really go with the triangle analogy. Strictly speaking, a triangle is but a visual simplification (projection) of the 3D coordinates. There is no actual triangle there.

Then, what sort of a graph does this formula plot and what does it mean? In the A, T, and S axes, the formula creates a hyperboloid, a sort of smooth hill like surface. If we cut it with a plane by fixing any one of our 3 parameters as a constant (e.g. ISO = 100), then the cross section is a hyperbola or simply a reverse proportion (e.g. A*T = const or A = const/T or T = const/A, the dependences well known to any photographer and explained in this thread numerous times).

So here you go, the answer to your triangle question geometrically is a hyperboloid that looks cool and represents the well known dependencies among the exposure parameters. I hope this helps

heheheh.. you're as bad as the rest of us. What happened to EV-L?

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Cheers, Craig
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I reserve the right to make mistakes in reasoning and logic as well as to change my mind anytime I wish. I also ask forbearance with respect to my typos. Please take a look at my gallery here at DPR.

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