NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Basics of computing sunrise/sunset
From: Douglas Denny
Date: 2009 Jun 22, 13:14 -0700
From: Douglas Denny
Date: 2009 Jun 22, 13:14 -0700
Further to the debate about looking at the sun through a telescope:- The question of brightness of image through a telescope at the eye with reference to viewing an extended object is only slightly more complicated than the case of a point source like a star, in that the source being extended presents a large evenly diffuse illuminated source as the object, and the light emerging through the exit pupil to the eye can be limited by vignetting - i.e. the restriction due to cut-off by exit pupil of the optics if the eye is not in the full cone of light emerging from the exit pupil. The magnification alters the case by the inverse square of the flux entering the telescope objective aperture. This does not preclude or modify greatly the argument about increased illuminace at the eye with a larger objective, and certainly not so with reference to sunlight and its damaging effects with normal magnifications encountered. Larger objective = more energy entering the eye (compared to eye pupil alone) still applies in _all_ cases except where magnification is so very high the field of view and luminance of the image is dramatically reduced. If the exit pupil of the telescope is less than the eye (hence no vignetting) then the apparent luminosity of the oblect divided by the apparent luminosity of the object viewed directly is proportional to the area of the objective divied by the magnification squared. i.e = a const x Area objective / Magnification^2 Hence as the magnification is increased the apparent luminosity of the image seen through a telescope reduces as the inverse square of the magnification - i.e. it becomes dimmer and rapidly so. This is a common sense effect as the area of view of the object is reduced as the field of view of the extended object is reduced - so the luminosity of the object seen is apparently decreased as the area is decreased. This is the reason amateur astronomers can look at a bright Moon with large magnification. Increased magnification reduces luminosity. The brightness of the Moon and telescopes is a specious argument however as it is not spewing out vast amounts of damaging I/R and UV and its luminosity is a mere tiny fraction of the sun's. Also note that with unity magnification of one (1.0) with a telescope, then the apparent luminosity of the image is again still a function of the area of the objective only, compared to the area of the eye pupil - similar to the special case with a star or point source. The problem with the sun is the luminous intensity is orders of magnitude greater than the Moon, and has the damaging I/R and UV content. As the objective lens has much greater diameter than the eye pupil the energy entering the eye is going to be increased as a function of the areas of aperture. It should be common sense to realise the enrgy entering a large objective of say, just 50 mm daimeter, is going to be much greater than that entering 6 mm diameter. I wrote the following in a private coversation about this to a friend on this forum: =============== Pupil diameter of an eye is about 6mm - an area of approx 28 sq mm. An ordinary binocular aperture is about 50mm diam, or 1963 sq mm. which is 70 times greater. So neglecting inefficiencies in the optics, if all light is transferred through the exit pupil of the telescope to the eye, the energy entering the eye due to the telescope is 70 times that entering the naked eye. Worse ....... this 70 times increase of illuminance is then focussed down in the eye to the foveal area which has a diam of 0.3mm which is 0.28 sq mm. Compare the ratio 0.28 to 1963 which is 1 to 7010 i.e. the telscope of 50 mm diam increases the flux at the fovea by 7000 times. ------------- There was (is still?) a religious sect in India who for some peculiar reason stare at the sun. They all go blind very quickly - that is with standard pupil size of 6mm diam. A telescope can blind in a matter of seconds - or less. You can get an idea of this in action considering an ordinary "magnifying" lens; i.e. bicovex glass lens and the burning of paper to make fire which I used to do for fun as a youngster. (Use glass - plastic lenses reduce I/R quite well). The magnifying lens produces a cone of light to a point (approx) focus. So the illuminance circle is getting smaller and smaller until it is a small image of the sun at the focus. the infra-red at this point is intense - I guarantee you will snatch your hand away quickly if you focus it onto your skin. You only have to move the focus away slightly to reduce the intensity quite rapidly to be able to stand it. Imagine this kind of focussed energy at the retina and you have some idea why it is so dangerous. ========================== Whilst it is true the setting sun is greatly attenuated, and people do look at it with the naked eye, to do so with a telescope is still putting oneself at risk which is unecessary. Potential long-term damage to the eye is still a known phenomenon other than the rather dramatic burning of a macular hole in the retina. Early cataract being one of them, and possible early macular degeneration. The simple rule is - don't put yourself at risk when you don't have to. Douglas Denny. Chichester. England --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---