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    Re: Mirages, was: Refraction
    From: Fred Hebard
    Date: 2004 Jul 17, 17:43 -0400

    On Jul 16, 2004, at 5:19 PM, Trevor J. Kenchington wrote:
    > Fred Hebard wrote:
    >> I am specifically wondering whether a ship could ever appear to sink
    >> below the horizon even though it actually was above it.  My
    >> understanding is that normally ships appear higher than they really
    >> are.
    > Fred,
    > I think you are missing one of the fundamentals of optics.
    >  The image of a ship that is created by a mirage, like the image of
    > your face when you look in a mirror, does not exist at the point where
    > you think you see it. Technically, it is a "virtual image". [Other
    > optical systems do create images where we think we see them -- a slide
    > projector, for example, does create an image, which we can see if we
    > place a screen at the right place (or else twiddle the focus knob on
    > the
    > projector to move the image to where we had already placed the
    > screen).]
    > Since the image is a virtual one, it cannot sink _behind_ the horizon
    > because it doesn't actually exist anywhere near the horizon.
    Shoot Trevor, OK the light rays emanating from the ship cannot reach my
    eyes because they are blocked by the earth.  But the image is still
    appearing to sink below the horizon.  Come down off your high horse for
    a bit; all of your examples are of objects below the horizon being
    visible or objects appearing to be higher than they really are.
    The ship is sailing away. The farther away it gets, the lower the image
    sinks.  First the ship is hull up, then only the sails or mast shows,
    then only the tops of the sails, finally nothing.  By simple geometry,
    the curvature of the earth is blocking a view of the ship: the earth is
    between you and the ship.
    Now, as the image is sinking, my understanding is that the real ship is
    normally lower than it appears, just as the setting sun is already
    below the horizon at sunset.  If you measure the height of a hull-down
    ship's mast for instance, assuming that you know the real height of the
    portion visible to you, your assessment of it's range will be in error,
    too short.  Is there ever a case when your assessment of it's range
    will be in error in the opposite direction, too long?

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