From: Leigh Palmer <palmer@sfu.ca>
Subject: Re: Binoculars, exit pupil size, etc...
X-Xxmessage-Id: <A7674E673B011C19@rs12-annex3.sfu.ca>
X-Xxdate: Wed, 30 Dec 92 21:02:31 GMT
Organization: Simon Fraser University
X-Useragent: Nuntius v1.1.1d16
Date: Wed, 30 Dec 1992 21:01:17 GMT

In article <1992Dec30.090406.1@stsci.edu> , gawne@stsci.edu writes:

>A question for Tom (or anyone else who cares to answer):  Do binoculars
>really form a virtual image?  You seemed to say that in your reply but as
>I understand virtual images they can't be imaged onto a sheet of paper
>placed at the focus.  I just checked Weidner's intro Physics text which
>seems to agree with my recollection.  I have often focused a binocular's
>image onto a sheet of paper or cardboard to check eye relief so this
doesn't
>square with my understanding of virtual imagery.

I'd like to answer the question of "virtual imagery". First I will make
an observation about this matter. The attribute of reality or virtuality
is not a physical property, it is a matter of convention alone. I will
speculate later on the reason for its having risen to the exalted status
it seems to hold in physics textbooks.

The convention has it that an image formed behind the imaging system has
a positive image distance and is thus characterized as a real image. It
is not important that such an image can be cast on a screen, and that
false idea has confused this matter for all my life. For example, the
image of a distant object which is formed by the objective lens of a
galilean telescope (or any other positive lens) is a real image. The
presence of the eyepiece lens prevents that image being cast upon a
screen but, by convention, does not change its character.

The image which one sees in binoculars may be real, virtual, or neither.
For the relaxed, "normal" eye (another convention) the focus on the fovea
is sharpest for objects located at infinite distance. Binoculars are
thought to be ideally adjusted when objects seen in them are focussed on
the fovea with the eye relaxed, so the image formed by the binocular of
an object at whatever distance is located at infinity. An image located
at infinity is neither real nor virtual, since it is representable as
either by merely changing the sign of the (infinite) image distance.

For those of us who are not "normal" the situation is different. I am
nearsighted, a myope. For me to view an object with binoculars and
relaxed eyes its image must be at a negative image distance, about 60 cm
in front of me. When I focus my binoculars they form a virtual image.

A farsighted person using the same binoculars would adjust them to form
an image at a positive image distance, perhaps a meter behind his head.
In that case the binoculars would form a real image.

The experiment to which Bill refers here is the location of the exit
pupil of the binoculars. It is, indeed, a real image, but it is a real
image of the binocular objective, not the object of interest in the field
of view of the binoculars. For an ideal instrument all of the light which
enters the objective (technically, the entrance pupil) is imaged in the
exit pupil. The exit pupil of any good pair of binoculars is at a
positive image distance behind the eyepiece. The exit pupil of a galilean
telescope is at a negative image distance, making such a telescope
inconvenient to use, since one would like to put one's eye at the
position of the exit pupil.

If this is all a matter of convention, why do we argue about it? The
answer, in my view, is that a big fuss was made about it when we took our
physics courses. It was possible to ask the question "Is the image real
or virtual?" and mark the answer unambiguously as "correct" or
"incorrect" without much thought or effort. We teachers like items like
that! I can (and have) constructed several quite diverse examples of
images which are neither real nor virtual by convention. I've never got
around to publishing this work, but a couple of the examples are quite
striking. I'll be glad to demonstrate them to anyone who visits me at SFU.

Leigh