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Recent discussions about danger to sight in looking at the Sun through the
telescope of a sextant have got me pondering about the physics and optics
involved. I have concluded that through a telescope the danger of a
retina-burn is no greater (and may indeed be much less) than when looking
at the Sun through a naked eye. This has surprised me, somewhat. Let me try
my arguments out and see if someone can find a snag and disprove what I
say.

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

The Sun subtends an angle of (damn near) half a degree. Looked at directly,
this gives rise to an image half a degree wide at the retina. If the focal
length of the eye is 15mm (a typical value, I understand) then the Sun's
direct image on the retina is about 1 mm diameter. We know that the Sun's
energy (light and heat) which passes through the iris, if focussed on that
1mm spot, can be  immensely damaging. That's what gives rise to retina
burns, which literally ARE burns, and can't be cured. Many old navigators
had such burns in their "sextant eye", and blindness would often ensue. The
worst instrument for causing eye damage was the cross-staff, until someone
had the idea to attach a bit of smoked glass to the upper end of the
cross-piece.

What would happen if you looked at the Sun through, say, a x3 telescope?
Well, the unescapable facts of life about optical instruments tell us this-
That for the telescope to put light into the pupil of the eye, opened to a
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 pupil of the eye. If the objective is bigger than that, any extra light
it collects will miss the entry pupil, being excluded by the iris. The
result is that at most 9x as much light (and heat) than before is passing
through the pupil (though we must allow for some losses of light and heat
in passage through the telescope's optics).

And what happens to that light? Well, it's divergence (the angular size of
the Sun's image) has been increased by the x3 magnification, to 1.5
degrees. Now it paints a disc-image on the retina which is 3x the size it
was before, so now there's a 3mm diameter image of the Sun on the retina.
This is a 9x greater area than the naked-eye image of the Sun was, over
which that 9x increased amount of light is now spread. So its intensity, in
terms of light-and-heat energy that falls on each square millimetre, is no
greater than it was with the naked eye, and less if we allow for energy
losses in passage through the lenses.

I think it may be true that most such retina damage is caused by heat
rather than by light, which is why they tell us that a nearly-black frame
of silver in black-and-white film is effective, whereas the same darkness
of colour film, created by dyes, does little to reduce the infra-red. I
wonder whether glass lenses in a telescope are more effective than plastic
ones in reducing the heat content of sunlight.

The conclusion, that a magnified telescope Sun image on the retina is no
more intense than a naked-eye Sun image, seems to contradict all my
axperience of a burning-glass, with which, as a small boy, I used to be
such a menace on a sunny day. I explain the distinction to myself like
this. 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.

If that's true, it should not induce any feeling of complacency when
observing the Sun through a telescope. Although it implies that a burn-spot
won't appear more quickly than with the naked eye, it also implies that any
such burn-spot will be correspondingly bigger. The lesson is, then, that
you could fry your whole retina in the same time that it would otherwise
take to fry a small spot!

The analysis above is presented rather tentatively. Optics isn't my
subject; but to me the conclusions seem inescapable. I would welcome
support or dissent from anyone.

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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