Diffraction Limit Discussion Continuation

Started Feb 21, 2014 | Discussions thread
Just another Canon shooter
Just another Canon shooter Senior Member • Posts: 4,691
Re: Check your maths

Jonny Boyd wrote:

Just another Canon shooter wrote:

Jonny Boyd wrote:

So where does delta_w become too small to notice a change in resolution? When delta_w < w_0.

What if that happens when delta_w/w_p<w_0 (which is approximately d(log w)<w_0)? Imagine all the colors then!

I don't have a maths degree, but I'm pretty sure you can't compare units with different dimensions, so asking if delta_w/w_p (dimensionless) is less than w_0 (length) is nonsensical.

It is, if you put there a constant that changes with the units, like the gravitational constant in Newton's law.

Let me revise it then, if R is the "resolution" in fixed units, why not dR/R^2<0.05. That would be d(log R)/R<0.05, i.e., the rate of change of R on a log scale. And yes, 0.05 would change if you change the units, and whether this is the right law or not, can be decided by experiments with people. It is not such a strange low if you think about it, it reflects the expectation that when you start increasing R too much, you notice that less and less. If you do not like log, I can replace it with your favorite function with a decreasing derivative.

BTW, I am still playing your game, in which I do not believe to begin with.

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