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Of course, it is the law after all.
I believe what you're really wondering is why do sources define the focal point as R/2 for incoming rays that are "close," and parallel to, the optical axis. I haven't found this anywhere else, but I worked out the intersection of the optical axis and incoming rays parallel to it just now.
For incident angles less that 60 degrees, the intersection is equal to:
R=radius
i=incident angle; this is in respect to the normal, as always.
r*cos(i)/[1+cos(2*i)]
Rounding to four decimal places, there is ~21.32 percent difference between the average of this and the R/2 method. It's ugly, but it's a lot easier. So, using the R/2 method will focus ~59.73% of the light captured. Very ugly, indeed.
This is all according to my own work, of which has never been reviewed. Interestingly enough, light with a 60 degree i will exit parallel to the optical axis (and r*sqrt(3)/2 opposite of it's side of entry).
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∙ 15y ago
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