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My first mailing on this topic had compared the Sun brightness seen through
a 3x telescope with Sun brightness seen through the naked eye.

Jared Sherman had responded that some optical instruments had much larger
objective lenses than the 3x15mm sextant telescope I had chosen as an
example, and that these were capable of putting much more light into the
eye. That is indeed true.

To my objection-

"There are snags with Jared's chosen example. Nobody, I suggest, would make
a 3x telescope with a 50mm objective."

he has replied-

> I didn't suggest anything of the soft. We've been discussing sextant
>telescopes and--from the wording of some of the posts--the larger issues of
>"telescopes" or optics in general. My comments were directed to the broad
>issue, that there are commonly available optics which folks may pick up to
>look at the sun, with objective lenses commonly ranging from 30mm (sextants)
>to 50mm (binoculars) and 80+mm (common spotting scopes and birding scopes)
>and none of these even touch the range of "telescopes" for general
>astronomical purposes. I think I've seen hundred dollar "astronomy" scopes
>at the WalMart with larger objectives, and they don't ask for any skill
>levels before selling them to the public.

What he says is correct. But what he has missed out is this-

To compress the light from a large objective into a small diameter (the
pupil of the eye), it's unavoidable that the telescope has to have a
magnification at least as great as the ratio of those two diameters. That's
why 6x50mm or 7x50mm are such common oculars, and why you never see a
3x50mm ocular. Much larger objectives can be used, but always, to go with
the larger diameter, they must have a greater magnification.

I had compared the brightness on the retina of direct-Sun, compared with
x3telescope-Sun. But if you go to a bigger objective, and therefore a
bigger magnification than x3, then that changes the calculated brightness,
because the bigger magnification gives a bigger image on the retina. For
example, if instead of my suggested 3x15mm telescope you used a 6x30mm
instrument instead, then the objective would then collect 4 times the
amount of light, pass it all through the pupil, and paint an image on the
retina which had 4 times the area. The surface brighness of the Sun image
on the retina remains unaltered, and exactly the same as it was for the
naked-eye Sun.

There seems to be no way round this, and I am grateful to Ken Muldrew to
putting a name to Liouville's Theorem, which appears to back up my
suppositions, though I haven't yet seen that theorem spelled out. I have a
textbook, "A Treatise on Light", by R A Houston (1938 edn.) which on page
359 shows that "the image of an extended object formed by a lens or mirror
can never appear brighter than the object itself", but without mentioning
Liouville.

Jared refers to the -
>lens made
>out of tissue (the cornea) which can be BURNED and damaged without any harm
>coming to the retina all the way in the back. If the spot of the the sun
>happened to focus and fall on the cornea itself--rather than back in the
>retina--then the full image from the lens, unreduced by the iris and pupil
>size, would be able to burn the cornea just like an ant under a child's
>glass.

Well, I did try to deal with the aspect of damage to the front end of the
eye, rather than to the retina, saying in my first posting-

"There's no doubt that with a single lens sunlight can be concentrated into
a small spot. For example, with the telescope example above, the light
intensity falling on and around the pupil will be 9x increased above the
naked-eye case. And so, if the eye surface or the iris itself are easily
burned by high intensity, that risk will be greatly increased when looking
through a telescope. However, the intensity of the light that gets through
the pupil to the retina itself, will not be increased."

Jared concludes-
>if there is any chance of
>damage at all--no matter how small--who among us would want to risk losing
>the vision in an eye, forever? Tha may be why the generic advice is simply
>never to look at it...

I don't disagree at all with Jared here, which is why my first posting
included these words-

"NOT, please be aware, that I am suggesting you should look directly at the
Sun, either naked-eye or through a telescope. Avoid both!"

He continued-
>...rather than trying to explain exactly how and when the
>threshold for dmaage is passed.

Well, I disagree most strongly with THAT sentiment! It is anti-scientific
obscurantism at its worst! Although it may indeed be true (and to me now,
the evidence is accumulating) that a telescope does NOT increase the
intensity of the Sun's image on the retina, only its size, it seems that
Jared would rather not know that.

George.

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contact George Huxtable by email at george@huxtable.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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