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Re: Cartesian Sign Convention for Optics



On 03/28/2003 02:40 PM, I wrote:

But the point is, the quantities that appear in
the thin-lens formula are not distances. They
can't be distances, because they have nontrivial
signs. Similarly, the "focal length" isn't
properly a length, because it has a nontrivial
sign.

Alas I shouldn't have said "sign".
Vectors don't have signs.
They have directions.
In D=1 the distinction is picayune, but we
might as well get in the habit of doing things
right.

I should have said that the object-position
vector and image-position vector have nontrivial
directionalities. Similarly the so-called "focal
length" has a nontrivial directionality.

================

And BTW:

You might be wondering about the units of
measurement for the vectors 1/a and 1/b.

If the position-vectors a and b are measured
in meters, then the reciprocal vectors 1/a
and 1/b are measured in diopters. A diopter
is a reciprocal meter.

1/a - 1/b = 1/f