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moonlight /again



I pondered the responses to Skip's moonlight observation.
I finally appreciated that John Mallinckrodt's response
was a model of insight: clear, straightforward, convincing.
I think this is sometimes called 'cogitation'.

Brian Whatcott Altus OK


Skip Kilmer writes:

>When one sees moonlight reflected from the surface of a lake, if the
>water is at all disturbed, the disk is stretched into a line.

/snip/

Why don't the
>randomly directed surface ripples make it just as likely that light
>hitting off to the side would reflect into our eyes?
>skip

At 04:14 PM 4/22/2003 -0700, John Mallinckrodt, you wrote:

This is a nice exercise in geometry. It is easy to see that, for
example, a 1 degree maximum tilt of the water surface toward or away
from the line of sight will produce a vertical deflection of the
image of 2 degrees above or below the "flat water" image and making a
"vertical" column that is about 4 degrees (or 8 moon diameters) in
length.

The harder part is determining what corresponding tilt of the surface
is required to deflect the image the same 2 degrees to either side.
The answer depends on the height of the moon above the horizon. I
find that when the moon is 10 degrees above the horizon, a tilt of
nearly 6 degrees is required. Furthermore, the required tilt
increases in roughly inverse proportion to the height of the moon
above the horizon so that when the moon is only 2 degrees above the
horizon, a tilt of nearly 27 degrees is required. That would
correspond to some very rough conditions on the water.

Alternatively, we can ask about the results on a calm night when the
ripples are restricted to no more than 1 degree of deviation from the
horizontal. We have already seen that this would produce an 8 moon
diameter "vertical" blurring. However the side to side blurring
would be just over one diameter with the moon 10 degrees above the
horizon resulting in a fairly well defined vertical column.
Furthermore, the vertical definition would only get more precise as
the moon gets closer to the horizon.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm