In article <sJYSd.3614$MY6.2120@newsread1.news.pas.earthlink.net>,
W. Watson <wolf_tracks@invalid.inv> wrote:

I'm looking in a microscope, and can see the object in the eyepiece from
a 1/10"
out to 3" pretty clearly. Of course, it gets smaller as I go out. Isn't this
called the depth of focus?

Are you talking about moving your head back and forth behind the eyepiece?
If so, that's simply the lens of your eye changing its focal length to
"accommodate" to the changing distance between your eye and the image that
you're looking at. It's the same reason why you can hold an object within
a range of distances from your eye and still see it clearly. For young
people this range of distances is usually, quite large. For older people
(like me!) the range is much smaller, which is why we need bifocal or
trifocal eyeglasses.

Perhaps it's how much I can move the microscope's
knob in and out and still maintain focus, which isn't much.

That's one way to describe "depth of focu" for a microscope.
Alternatively, it's the range of object positions, for fixed lens
position, that produces acceptably sharp images. Note "acceptably" rather
than "perfectly".

If my head movement example is wrong, then why can I clearly see the
image over a sizable range? My eye is a lens, so isn't there an area
(range) of focus?

See above. The lens of your eye can change its shape and therefore its
focal length. As you get older this ability decreases.

W. Watson wrote:

I'm looking in a microscope, and can see the object in the eyepiece
from a 1/10" out to 3" pretty clearly. Of course, it gets smaller as I
go out. Isn't this called the depth of focus? Perhaps it's how much I
can move the microscope's knob in and out and still maintain focus,
which isn't much. If my head movement example is wrong, then why can I
clearly see the image over a sizable range? My eye is a lens, so isn't
there an area (range) of focus?

It's not entirely clear what you are doing, but "depth of focus" or
"depth of field" traditionally means the image plane is at a constant
position and the object plane moves. So, the depth of field of the
microscope would be how much you can move the sample up and down,
keeping your head still, and have the sample be in focus.

Eyes have a smallish depth of field due to their focal length (f#/ of
about 3 - 4), and the ability to change the focal length of the lens by
using musculature.

I see a formula for depth of focus that involves the wave length
divided by a quantity involving the sine square. Does this formula
have a name, or is named for someone? I'd like a source where it is
derived of discussed. The web page I'm looking at calls in the depth
of focus diffraction formula.

That quantity is called "numerical aperture" and is generally the most
important specification of a lens (aside from quality of manufacture).
Deriving that formula (d = l/NA^2, I believe) is not simple, and is only
valid for the paraxial approximation. For large NA lenses, the formula
is modified somewhat.

Born and Wolf have a derivation of the paraxial approximation formula.
To be sure, depth of focus is somewhat nebuluos, requiring someone to
decide exactly at what point the object is no longer in focus. Attempts
to quantify the relationship, for example by using the Struve ratio, are
moderately successful.