I'll give it to RiffRaff, since he was the first to note Ben Franklin. But ParadigmShifter did nail the curiousity.
RiffRaff's up!
I'll ask another maths question then.
If you have a chessboard and cut out 2 opposite corner squares, can you cover the dissected board with 2x1 dominoes (overlapping not allowed). If you can, draw a diagram. If not, give a proof.
Distortion
Suppose you make an image of an object by collimating (i.e. making a beam where the rays are parallel) the light coming from the object and then focusing the beam again on the image plane.
What happens with the image (beside obviously getting darker) , when you put a disk in the center of the collimated beam that:
a) has a smaller diameter than the beam?
b) has a bigger diameter, but a hole in the middle?
I'm assuming (since you didn't specify) the object being imaged, the beams of light and the disks are pretty big, in which case (a) would have the image with a big black circle in the middle, and (b) would only have the middle part of the image.
...
GoodGame said:Well, first off light can bend along an object (seen from holding a pencil up to a lamp). Probably the disk will absorb some of light that hits it, scatter some more, but some light will bend along the filter edges and still hit the image plane.
GoodGame said:I think the in the first case the center of the image will be darker and more obscure relative to the outer edge of the image.
In the second case, I believe the light will just be more focused throught the filter, and the image will be unaffected, except that it will be much smaller than it was before the disk was placed, due to a smaller diameter of light reaching the image plane.
Will there be a colour shift because of refraction through the lenses you're using?
It polarises the light? I'm guessing (a) and (b) polarise the light along different axes?
It filters the colours?