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    Re: Sextants with Polarizing filters
    From: George Huxtable
    Date: 2006 Jan 27, 10:34 -0000

    Bill has asked-
    Off topic, I have always wondered about the order of the f-stops.  The
    relationship is clear enough: relative increase in the radius of the
    aperture to double transmitted light.  It has always struck me as strange
    given aperture dimensions that 1, 1.4, 2 etc are the largest openings, while
    45, 64, and 90 are much smaller.  An inverse relationship.
    Any history buffs out there than can explain that?
    response from George-
    The ability of a lens to illuminate an image depends on the diameter d of the lens, and its focal
    length f. It's actually proportional to (d / f) squared. (d / f) is simply the angle that the lens
    subtends, as seen from the image plane, expressed in radians rather than degrees (a radian is about
    57 degrees).
    About the most efficient lens you will come across in an ordinary camera has a diameter equal to
    about 0.5 f when wide open (so aperture = f / 2). It can be "stopped down" to a smaller diameter of
    say 0.35 f  (so aperture is f /2.8 ), which will let through about half as much light. Or further,
    to 0.25 f  (so aperture = f / 4) in which the light is one quarter of the original. Simple cheap
    cameras often start with a lens restricted to that size (f / 4) which can be subsequently stopped
    down further. All this, I'm sure, Bill is painfully familiar with.
    Usually, in a camera or other optical device, the focal length is fixed  ( the focus being variable
    enough just to allow for focussing of nearish objects) and the thing that can be readily varied is
    the aperture (by stopping down, or choosing different lenses). So the different apertures or lenses
    that could be chosen, assuming that the focal length f remained unaltered, were properly marked f /
    2, f / 2.8, f / 4, and so on. In the days before 35mm film stock became a standard, the focal length
    might vary quite a lot from one camera to another, but it didn't matter. The f-fraction told you all
    you needed to know about the light that was needed on the scene, as long as you knew the "speed" of
    your film.When the lens aperture was marked "f / 4", each of those characters had a meaning, which
    was " focal length divided by 4". To make sense of it, perhaps it should be spoken as "f over four".
    In my young days, ancient history to most, that was the way we referred to apertures, lenses, and
    stops, and that was the way we THOUGHT about them. All reasonably logical.
    But then, over the years, much of that sense has been taken away, by abbreviation. First, the
    initial "f" was dropped, so apertures were marked "/ 4", "/ 5.6", and so on; the understanding being
    that you had to think of it as a ratio of "one quarter", etc. Then the "/" was dropped, so all you
    ended up with was an increasing series of numbers, 4, 5.6, 8, and so on, providing progressively
    decreasing brightness: the illogicallity that Bill complains about. All in the name of progress, no
    doubt. It makes those numbers easier to fit into the aperture ring of a tiny camera, of course, but
    much of their MEANING has been obscured, so now they can even puzzle such an expert in the field as
    Bill clearly is.
    Me, I don't pretend to be any more than a very amateur camera user, but that's my memory of how
    things were.
    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ----- Original Message -----

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