How do I calculate the height of a cross section of a circle?
I'm working on an LED lighting project and have discovered that it involves a little math...
I'm mounting LEDs to plexiglass facing away from the surface I want lighted. I'm looking at cutting a cross section of PVC pipe as a reflector to diffuse the light, so that the light shining through the plexiglass appears smooth and even (ie you can't see bright spots from individual LEDs). I need the reflector to have a very low profile. So now comes the math - what diameter of PVC pipe do I buy in order to obtain the desired cross section?
B, as the base of my cross section, is 2 inches. I'll be playing with different numbers for H, but let's start with 1/2 inch. Is it even possible to determine D (the diameter of the circle)? If so, what would be the equation to do so?
Similar to this question, but I'm working with a circle, not an ellipse, so mine should be easier. I hope :)
If I start with a circle of D=2, then B=D=2 and H=1. Pretty simple. If I want H to be half, then my (very unpracticed at math) analysis is that D should be double. Am I even on the right track? If so, then if I want H=1/4" I would need a pipe with diameter 8"....
$\endgroup$ 11 Answer
$\begingroup$Is it not just using the Pythagoras:
$(\frac{B}{2})^2+(\frac{D}{2}-H)^2=(\frac{D}{2})^2$
Thus:
$D=\frac{\frac{B^2}{4}+H^2}{H}$
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