A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Telescope danger to sight. Was: Venus transit ...
From: George Huxtable
Date: 2004 May 12, 23:20 +0100
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 >attention. > >
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 >2mm. >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. George. ================================================================ 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. ================================================================