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Re: [OM] f/0.x lenses

Subject: Re: [OM] f/0.x lenses
From: Joey Richards <bigjoe@xxxxxxx>
Date: Thu, 11 May 2000 19:10:07 -0400
pizzuto <pizzuto@xxxxxxxxxxxxxxx> wrote:
> May I ask a technicality?
> 
> I always understood the f number to refer to the ratio of the actual
> scenery light intensity appearing inside a lens.  Ex: f2 would let in
> 1/2 the light intensity.  Ergo, wouldn't f < 1 imply that light
> amplification was taking place.
> 
> Or am I the shame of the Oly list with my wrong understanding of the f
> number... grin..

Unfortunately, you have a wrong understanding of the f number, though
I would not go so far as to say this makes you the shame of the list.
Maybe shame of your block, but not the whole list.  :-)

The f number is the ratio of the focal length of the lens to the
aperture diameter.  (I think it is diameter -- it may be radius, though, in
which case you should multiply by 4, but that's incidental)  Thus,
the designation f/2, f/4, etc -- f = focal length, so f/2 is 
focal length divided by two.

Because the amount light that passes through the lens is proportional
to the _area_ of the aperture, intensity goes as 1/f^2 (or, to sound
fancier, goes inversely as the square of the f number).  As a result,
if you double the f number you divide the intensity by 4.  In order
to double the intensity, you have to sqare-root-double the f number,
or multiply it by 1.4142135...

Thus, the f number sequence:

 1.0  =  1.000
 1.4 ~=  1.414  =  1 * 2 ^ 0.5
 2.0  =  2.000  =  1 * 2 ^ 1.0  ~=  1.4 * 1.414
 2.8 ~=  2.828  =  1 * 2 ^ 1.5  ~=  2.0 * 1.414
 4.0  =  4.000  =  1 * 2 ^ 2.0  ~=  2.8 * 1.414
 5.6 ~=  5.657  =  1 * 2 ^ 2.5  ~=  4.0 * 1.414
 .
 .
 .


Note that all these intensity fractions are relative to the
brightness passed by a lens at f/1.0.  While this is related
to the "actual brightness" of the scene, there is some
prefactor there that we don't know (well, more accurately,
that *I* don't know).  When a light meter is calibrated, it
is being calibrated to this prefactor.  

Thus, you can make the f number less than 1 if you like -- you
are not generating power, you are just letting more light through
than would the (basically arbitrary) lens whose aperture was the
same diameter as its focal length.  You can go on increasing the
aperture infinitely.  Yes sir, you could get arbitrarily close
to an f/0 lens.

Obviously energy must be conserved (well, maybe not obviously,
but Einstein and Feynmann said it, and now I'm saying it, so you
should believe it :) ), so you _cannot_ _ever_ get more power
to the film plane than is being emitted by your image sources.
What we have been assuming in the above is that the total power
coming in and reaching the film (which is what we mean when we
talk about intensity) is constant over the aperture.  That is
why we say that intensity is proportional to aperture area.
However, once your aperture becomes of appreciable size compared
to its distance from the objects in your scene, this assumption
becomes invalid -- more power is transmitted through the center
of the aperture than at the edges (aha!  one origin of 
vignetting!!).

Thus, for most terrestrial activities, a f/(1e-10) lens and a
f/(2e-10) lens would exhibit the same brightness -- there is
basically no power coming through the aperture out at the
edges of the f/(2e-10) lens so you get no additional power
coming in through the region of the f/(1e-10) outside the
radius of the smaller huge aperture.

An f/0 lens would capture *all* power emitted toward the lens
(and not obstructed) anywhere in the universe.  Its depth of
field would be pretty shallow, to say the least.  :-)

So, anyway, you can quite truly have wider apertures than 1.0.
They would be f/0.7, f/0.5, f/0.35, f/0.25, ...

hope that's helpful.  Hm, no, I think helpful would be the
wrong word.  Confusing is probably more like it :-)

joey


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