John, I clicked 'send' on my last message without adding the detail of the
formula!

The basic formula is actually f=(s^2)/(L), where
f is the focal length, s is the radius of the (infinitely thin!) hole and L
is the wavelength of the light.

Sunshine has a representative wavelength of 550 nanometres. so that the
formula can be written:

s=SQRT(f)*SQRT(550)
So, D the diameter is given by
D=2*SQRT(f) *23.452, or
D= 46.904*SQRT(f)

But all these are in nanometres so we need to multiply by 0.001 (actually
SQRT(0.001^2) to get millimetres. Thus

D=0.046904*SQRT(f)

That's where the 0.047 comes from.  It gives a way for calculating how a
near-perfect shadow sharpener should work when used on sundials.

Patrick





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