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    Re: Nav light colors and ranges
    From: George Huxtable
    Date: 2003 Oct 17, 16:00 +0100

    Jared Sherman said-
    
    >The candela is the luminous intensity, in a given direction, of a source
    >that emits >monochromatic radiation of frequency 540 x 1012 hertz and that
    >has a radiant intensity in >that direction of 1/683 watt per steradian.
    
    Presumably, that was intended to read 540 x 10-to-the-power-12 Hertz:
    anyway, it's not very helpful to an understanding of the brightness of our
    nav. lights. If you think of a candela as being, roughly speaking, the
    brightness of 1 candle, you get a rather clearer picture, which is good
    enough for most purposes.
    
    Jared goes on to say-
    
    >The steradian of course will be instantly recognized by all list members.
    >It allows for a detection instrument which is placed xx meters away from
    >the light source with an specific area of the light source being read,
    >i.e. if a cone of light from that light source is allowed to form a
    >circular area on a sphere xx meters away from that light source, the
    >brightness of that circular area can be tightly defined and measured,
    >requiring nothing more than placing a special light meter next to the lamp
    >which is to be measured.
    
    Jared's definition of a steradian, here, is quite incomprehensible to me,
    though that could be my fault rather than his.
    
    Trevor Kenchington seemed to concur-
    
    >Not sure about your explanation of a steradian either. From unaided (and
    >so unreliable) memory, it is the 3-dimensional angle swept out by
    >rotating a 2-dimensional angle of one radian. A nice unit for a formal
    >definition of a candela but not, I would think, very relevant to the
    >actual measurement of the brightness of a light.
    
    Unusually for him, Trevor's memory has let him down here. The steradian
    isn't defined that way. If we have a sphere 1 metre in radius, and draw a
    cone from its centre that intersects its surface, and encloses an area of 1
    square-metre of that surface, then the solid-angle of that cone is 1
    steradian. It could be applied in the same way to shapes other than the
    cone, such as a pyramid. In the case of a cone, my own calculation (so it
    could well be wrong) indicates that it would require a half-angle (i.e.
    between its axis and its edge) of 32.8 degrees; very different to what
    Trevor suggested.
    
    Because, as we learned at school, the area of a sphere is 4 x pi x (r
    squared), there are 4 x pi, or about 12.5, steradians in a complete sphere,
    which is the biggest solid-angle that's possible. The lumen is the amount
    of light that passes through a square meter at a radius of 1 meter from a
    standard candle (candela): that is, in one steradian. Presuming that a
    candle emits, roughly speaking, the same amount of light in all directions,
    then a candle emits altogether about 12.5 lumens.
    
    The lumen is an example of an original unit that was tinkered-with
    ("rationalised" was the word then used) in order to avoid such factors as
    4pi being necessary in some calculations. Unfortunately, this implied that
    a factor of 1/4pi often became necessary in other calculations, and added
    much confusion, which persists to this day. It may be best to ignore lumens
    for our purpose here.
    
    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.
    ================================================================
    
    
    

       
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