Re: Private Universe and the Seasons

[Bob LaMontagne <rlamont@POSTOFFICE.PROVIDENCE.EDU>]

There's no actual convergence with a pinhole - it's a passive device. I
think the 'penumbra' referred to is just the fact that a large pinhole
will produce a circular image for a point source object. My comments
were strictly for a true pinhole with a negligible diameter compared to
the size of the final image. Since each point on the original object
will produce a circular image due to the finite size of the pinhole, the
final image will not look sharp because of the overlapping circles.

As far as 'not totally parallel', a 1 cm 'pinhole' at 150 billion meters
from the sun produces a divergence from totally parallel (for a point
source on the sun) of only 6.7x10(-14) radians or 3.8x10(-12) degrees -
totally negligible compared to the 0.5 degrees subtended by the sun.
Therefore a 1 cm pinhole produces a 1 cm circular image of a point on
the sun's surface. But the entire sun will produce an image which is
0.5/57.3 radians - or 8.8 cm at  distance of 10 meters from the pinhole.
This would be a fuzzy image because of the large pinhole.

Bob at PC

Chuck Britton wrote:
> Hugh - or maybe someone else -- mentioned both umbra and penumbra
> cones. One converges and the other diverges. For a finite sized sun -
> including rays not totally radial or totally parallel - won't BOTH of
> these produce a pinhole 'image'.
>
> At 7:42 PM -0400 9/21/03,  Bob LaMontagne wrote:
>
> > Hugh Haskell wrote:
> > >  Doesn't the size of the spot from a pinhole camera depend on how far
> > >  away from the aperture you place the receiver? I would guess that the
> > >  clearest image would occur somewhere near the point where the
> > >  "umbral" rays cross. If you take the image size at that point to be
> > >  the diameter of the penumbra, it will necessarily be larger than the
> > >  aperture in the case where the rays are slightly converging, as they
> > >  are from the sun.
> >
> > The pinhole spot, as well as the image from any lens used, subtends 1/2
> > degree, same as the sun itself. As you get further from the pinhole, or
> > use a longer focal length lens, the image gets larger, but still
> > subtends 1/2 degree.
> >
> > Bob at PC
>
> --
> Chuck Britton                                   Education is what is left when
> britton@ncssm.edu                       you have forgotten everything
> North Carolina School of Science & Math         you learned in school.
> (919) 416-2762                                  Albert Einstein,        1936