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    Re: Telescope danger to sight. Was: Venus transit ...
    From: George Huxtable
    Date: 2004 May 12, 23:20 +0100

    Jared Sherman said-
    >George, I'm wondering if you glossed by something that deserves further
    >certain diameter (say 5mm) it can collect that light only from an area of
    >the objective which is that same diameter, multiplied by the magnification.
    >So that's an objective of 15mm diameter, in this case, or 9x the area of>
    >The human eye typically has a diluted pupil of 5-6mm diameter, and rarely
    >more than 7mm. When contracted against bright light, that drops to something
    >like 1-2mm. (I'm less familiar with the fully contracted size.)
    >So, a human eye viewing the sun has an "onbjectve lens" with a diameter of
    >Compared to your telescope's objective lens of 15mm.
    >But the scope on many sextants is well wider than 15mm, easily in the 30mm.
    >range. And "cheap" binoculars rapidly push past 42mm to 50mm objectives
    >while common telescopes used by birders here are 77-80+ mm lens now.
    >The comparison then is of the human eye, gathering light, IR and UV
    >included, from a 2mm circle to a telescope objective gathering light from a
    >50mm objective. There's an incredible amount more light being gathered, and
    >even "cheap" coated optics boast a 95%+ transmission factor.
    >Perhaps this is all that is needed to explain the warnings?
    Thanks for Jared's contribution, but I think he may be missing the point.
    But if he thinks I misunderstand what he says, I hope he will argue back.
    As I hope my last message made clear, it's not a matter that I am
    completely confident about, and I'm ready to be persuaded otherwise. But
    not (yet) by Jared's argument.
    Let's accept Jared's assumption that, it being a sunny day, the observer's
    pupil has shrunk down to 2mm dia
    And now, let's consider a x3 telescope with Jared's suggested objective of
    50mm dia. Actually, I think one would be unlikely to come across such an
    instrument with a magnification of x3, for reasons that may become clear,
    but let's make that assumption anyway.
    We can compare the two situations, of with-telescope and naked-eye, in
    terms (in both cases) of the total sunlight energy which would be falling
    on a 50 mm dia disc, the size of the telescope's objective.
    That objective collects (50/2) squared times as much light as the eye pupil
    would collect, or 625 times as much, which is I think Jared's point. But
    where does that light go?. It would be shrunk into a light-pencil which was
    one-third of the diameter of the objective (because that shrinking by three
    unavoidably goes with the x3 magnification). So the light exiting the
    telescope eyepiece has a diameter of 50mm/3 or 16.7 mm, provided the
    eyepiece has sufficient diameter to let such a wide pencil through.
    So, we have a light-beam exiting from the telescope, 16.7mm wide, impinging
    on the eye. But remember, the eye pupil, we assumed, was only open to 2mm
    dia. So most of the light will strike all round the pupil and the eye and
    be lost, and only a tiny fraction of that wide beam of light will enter the
    eye. What fraction? Well, the area of the pupil divided by the area of the
    light-pencil, or (2/16.7)squared, or 1.44%. The rest will miss the tiny
    hole. And what area of the retina does that light fall on? A circle 3mm in
    dia, the Sun image magnified by 3
    Now, take the telescope away, so direct sunlight shines into the pupil,
    which has 2mm dia. We already worked out that this would be only 1/625 of
    the total light that would otherwise have fallen on the telescope
    objective. But now this light is concentrated into a retinal area of only
    1mm dia, because now there is no magnification.
    So we take 1/625 of the incident light, but allow an increase in this case
    by a factor of 9, because the light is concentrated into a retinal patch 9
    times smaller. And we get
    9 x  1/625  or 0.144, to compare with the figure 1.44% we arrived at for
    the telescope: Exactly the same, of course! The brightnesses in the two
    cases are the same, the only difference being that the telescope gives a 3x
    bigger (not brighter) image. And we have ignored any loss of heat and light
    in passing through the telescope.
    There are snags with Jared's chosen example. Nobody, I suggest, would make
    a 3x telescope with a 50mm objective. Even if it possessed an eyepiece
    16.7mm diameter, to let out all the light that went in, nobody has an eye
    in which the pupil can expand to anything like that diameter, to take in
    all the light that emerged. Instead, telescopes are usually designed to
    match the expanded night-time eye-pupil of say 8mm. In that case, with 3x
    magnification, an objective bigger than 24mm would be pointless, and to
    make use of a 50mm objective, the magnification would need to be 6x.
    But in daylight conditions, when the pupil has closed down to a much
    smaller diameter, only a tiny fraction of the incident light can get in, as
    shown above. The iris is doing its job. A large-aperture objective is quite
    wasted, under those conditions.
    contact George Huxtable by email at george---.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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