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Bill you wrote:
"My contention is that a  optically perfect shade with faces parallel will
still offset the ray if not  perfectly perpendicular to the ray path.  You
are probably correct that  the offset is negligible in practice, but
nonetheless does exist."

Frank responded:

"So  experiment! Get a piece of flat clear glass, and hold it in the light
path.  Rotate it. Tilt it 45 degrees to the light path. Then try
perpendicular to the  rays. Does it change the alignment of direct and
reflected images in your  sextant? There's nothing like experimental
evidence to constrain one's theoretical musings.

Here's another: No sextant involved. Hold a piece of  flat glass close to
some text on a page at normal reading distance. Rotate it.  Does the text
appear to shift from refraction (it should)? Now hold that same  piece of
flat glass up in front of some distant scenery. When you rotate the  glass
as before, do objects shift back and forth (they shouldn't)? TRY this
experiment and see if you agree with my should/shouldn't comments. Then work
out the theory...
Evidence constrains theory."

Frank

Tried the "no sextant" version of the experiment you proposed.  I used a
1/2"-thick piece of float glass with polished edges (I generally us it with
sandpaper adhered to it to lap plane blades and bottoms, and chisel backs).
The glass thickness near the edges was checked with a micrometer to verify
that they were parallel.

I then viewed a table edge at about 3 feet, a sidewalk edge about 10 feet
away, a rooftop about 100 yards away, and later the moon.  I used both the
left and right vertical edges of the glass, then flipped the glass end for
end and repeated for each viewing.

The glass was rotated from approx. perpendicular to the line of sight to
approx. 15d to the line of sight.  I attempted to keep the position on the
glass where the images were equidistant from my eye, and used the dominant
eye only.

I preface the following with the caution that there were no reasonable
measurement practices in place.  Displacement was judged by eye, and the
angle of the glass to the line of sight was hand held and at best
approximate.

Trial 1, Wednesday eve

In all cases, from the table edge to the moon, there was marked displacement
of the line/object halves viewed through the glass vs. the direct view
(table edge, sidewalk edge, and moon) as the glass approached a severe angle
(closer to parallel than perpendicular) to the line of sight.  The moon
halves were displaced by about 1/4 of its diameter (approx. 7') as the glass
reached a severe angle (approx. 15-20d off the line of sight).

Gauging displacement by the difference between the glass and air images by
distance along the glass edge, the amount of displacement appeared to be
about the same for far and near objects.  I again caution that angles were
approximate, and foreshortening was compensated for by eye.

Trial 2, Thursday afternoon

Same methodology as trial 1, but paid closer attention to the final angle of
the glass in relation to the line of sight.   A number of objects from 3
feet to 200 yards were observed, including a table edge, patio edge, roof
lines, and power lines.  In these observations the displacement appeared to
diminish with distance, but was still easily visible at all distances.

All I can safely conclude is that refraction is still with us (thank
goodness, I have a lot invested in camera lenses ;-)  Currently I am
considering how I can use photo clamps, articulated arms, tripods etc. to
set the angle of the glass to the line of sight consistently for subjects at
different distance, as well as a method to measure the offset.

So at the moment, my muse, the "should" does, and the "shouldn't" does (to a
magnitude related to the "should" yet be be determined).  Theory will follow
experiments with greater controls in place.

Bill

   

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