Patrick Powers wrote ... 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.
I would express this a bit differently, since a pinhole does not form an image in the sense that a lens does. Consider different pinholes imaging the sun on a plane at a fixed distance. The images are all the same size, but which one is sharpest? The images from the biggest pinholes are fuzzy by the size of the pinhole. But if you make the pinhole too small, then diffraction takes over and the images get blurry again. Patrick's formula tells you about what compromise you need to make to get the sharpest image. But remember that sharpness isn't everything. In particular, the smaller the pinhole the dimmer the image. If brightness is a problem, you might want to make the pinhole a few times bigger than this, particularly for large dials. If the pinhole size is fixed and you vary the the projection distance, the image gets fuzzy at short distances. At distances above that given in Patrick's formula, the sharpness doesn't improve much. near-perfect shadow sharpener should work when used on sundials. --Art Carlson -
