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    Re: Basics of computing sunrise/sunset
    From: Paul Hirose
    Date: 2009 Jun 19, 19:10 -0700

    douglas.denny{at}btopenworld.com wrote:
    > If this was not so - explain please why it is that stars invisible to the 
    naked eye of aperture diam 6mm - because they are too faint (intensity too 
    low to stimulate the retinal cells),   become sudenly visible with a 
    telescope of aperture say, 100 mm diam?
    That occurs because a star is a point source. Binoculars don't make it
    look larger, but they gather more light. Since more light is
    concentrated on the same area of retina, you can see a star which would
    be invisible to the naked eye.
    An extended object such as the Moon behaves differently. Its image on
    the retina responds to magnification. Suppose you're using 7x35
    binoculars. They gather 36 times more light than a naked eye with a 6 mm
    pupil. But due to the 7x magnification, the image on the retina has 49
    times more area than the naked eye image. Consequently, extended objects
    look dimmer!
    This is effect is minimized if the binocular exit pupil is at least as
    large as the eye pupil. For example, suppose the binoculars are 7x50s. A
    6 mm eye pupil utilizes 42 mm of the objective lens. That diameter
    gathers 49 times more light that the naked eye. The light is
    distributed over an image with 49 times more area. Therefore, the Moon 
    appears as bright as with the naked eye (less the small amount of light 
    lost in the optics).
    Amateur astronomers are familiar with this phenomenon. Increased
    aperture doesn't make nebulae look brighter. They just look bigger.
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