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    Re: Basics of computing sunrise/sunset
    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
    
    
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