Re: moonlight

[Jack Uretsky <jlu@HEP.ANL.GOV>]

        Think of the ripply surface as a diffraction grating with "orders"
of reflection.

On Tue, 22 Apr 2003, John Mallinckrodt wrote:

> 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. I've
> > always thought of this as diffuse reflection from the rippled
> > surface, and as I think about it, I can't satisfy myself why the
> > light should be concentrated "beneath" the moon. 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
>
> 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

--
        "What did Barrow's lectures contain?  Bourbaki writes with some
scorn that in his book in a hundred pages of the text there are about 180
drawings.  (Concerning Bourbaki's books it can be said that in a thousand
pages there is not one drawing, and it is not at all clear which is
worse.)"
                                        V. I. Arnol'd in
                                Huygens & Barrow, Newton & Hooke