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[Phys-L] Re: pinhole camera



Pamela L. Gay wrote:

In an idealized situation you are able to focus closer using a pinhole
because only one light ray from any given point on the object hits the
lens of your eye. Since there is only one light ray there is no problem
with focusing - the lens acts to redirect the rays not focus them and
there is an in-focus image at all distances from the lens. This is why
so many diagrams showing the eye and a pinhole negate the effects of
the eye's lens when doing ray tracing (which really mucks up students,
BTW).

With a pinhole, magnification the image size is proportional to the
object distance, such that if the pinhole is half way between your eye
and the object, there is zero magnification, and if your eye is twice
as far away the object will appear twice as large. I have to say that I
have never been able to actually see this, but this is what the math
claims, and I blame my inability to see through a small enough pinhole.




Since I'm working on a pinhole lab for next semester, I have a good excuse
to play around with this.

I tried drawing a diagram that assumes a point pinhole (no diffraction) and
an eye with lens having focal length f and a finite sized pupil. The size
of the pupil limits how much of the object that you can actually see. That
is, the rays from the pinhole to the edge of the pupil determine what you
see. Mindful of the first paragraph above, I wanted to see where the rays
went after going through the eye lens. I assumed the thin lens equation
and found the location of the image of the pinhole. Then, I drew rays from
the image of the pinhole (found assuming the thin lens equation) to the
edges of the pupil and continued them to the back of the eyeball, to find
the actual image size on the retina. I assumed that the eye lens was
relaxed, so the length of the eyeball was also f (no myopia). When I did
the geometry and used the thin lens equation to find the ratio of the image
on the retina to the size of the object that could actually be seen, I
found it to be f/L, where L is the distance from the pinhole to the object.
Everything else cancelled out.

Michael Burns-Kaurin
Spelman College
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