NavList:

   

Reply

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@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.
================================================================

   

Reply