Here is one of the best "with the hands" explanation of the function an aperture. I found it in EOS list and it was written by Gary W. Sims :
"As you've probably heard, a very small hole in a surface like a thin wall
will display a focussed image (of a landscape say) on another flat surface
placed behind the wall. No lens is required. That's called a "pinhole
camera" in English. Basically, the light from any given part of the scene
has only one path to follow through the hole to the image plane behind the
"wall."
Actually, many paths exist, but they are so tightly grouped together that
they fall within so small an area on the image that it appears to be in
complete focus without help from a lens. The smaller the hole, the better
this appearance of focus. (Up to a point. Different topic.) But a small hole
admits little light. So the scene must be in bright sunlight, and the area
behind must be a fairly dark room for our eyes to pick up the faint image
projected. Most film is less sensitive than our eyes, so the problem is
worse when we want to capture the image for posterity. So we must make
the
hole bigger to capture enough light.
When we make the hole bigger, light from any given portion of the scene
has
more paths to follow. The optics of a lens bring each of those paths to the
same point on the image plane -- or that's what we try to accomplish. The
bigger the hole, the harder the problem of designing a lens that will bring
each path to the same point for the three critical frequencies of light.
(Light of different frequencies is refracted by a different angle through
any given optical material.)
A factor you may not have noticed yet is that lenses with longer focal
lengths tend to have smaller maximum aperture numbers. That arises from
another effect. A lens of short focal length has a wide angle of acceptance
of light. That's roughly a right angle (90 degrees or Pi/2 radians) for a
"wide-angle" lens. A "standard" lens takes in a little less than 45 degrees,
and a very "long" lens is down around ten degrees acceptance angle. The
wide
lens is accepting light from most of the scene. The "standard" lens accepts
well under half the light that actually reaches the lens, and a long lens
accepts almost none of the light.
Of course, that's our intent. We use a lens of longer focal length to
restrict our image to a smaller part of the scene. But the effect of
accepting light from so little of the scene is that it takes a bigger hole
to capture enough light from that part of the scene to expose the film.
Picture it this way: The film is the same size, but the part of the scene
that must provide light to expose that film area is much smaller when we use
a longer lens. That means the hole must be bigger if the focal length is
longer if we want to expose the film in the same length of time.
If we measured aperture in millimeters, photographers would go crazy
trying
to compensate for the focal length of each lens to figure exposures. So we
use a ratio. We say that a lens has an aperture of f/4 to mean that the hole
is 1/4 the focal length. So a 50mm lens (standard in 35mm format) at f/4
will have a hole 50/4 or 12.5 mm across. At the same aperture number, a
100mm lens will have a hole of 100/4 or 25mm diameter. That gives the
longer
lens a hole with four times the area, so it can capture the same energy from
an area of the scene that is four times as small.
Incidentally, when you price zoom lenses, you will notice that expensive
zooms have a single maximum aperture number, like the Canon 28-70mm,
f/2.8L
that costs about U$1350. (The L stands for lust I understand.) Less
expensive zooms, like the Canon 24-85mm (at U$350) have a range of
aperture
numbers specified. For that example, the range is f/3.5 to f/4.5.
That might give the impression that the less expensive lens closes down its
aperture as it zooms, but in fact the opposite is happening. The hole
actually expands from about 7 mm at the short focal length to 19 mm at the
longest focal length, but the aperture ratio is decreasing because the
optics are limited in the size hole they can properly focus. To hold an
f/3.5 aperture at the long lens the hole would have to be 30% wider, or 24
mm across. The professional class lens starts at a 10 mm hole -- already
half as big as the less expensive lens ever reaches -- and it expands to a
25 mm hole at the long end. Canon breaks off the short zoom at 70 mm, but
they have a 70-200 mm that picks the range at the same aperture ratio of
f/2.8. When that other lens reaches 85 mm focal length at f/2.8, it's hole
is over 30 mm across. This is more than half again as wide as the 19 mm
hole
that the optical design of the less expensive lens can tolerate. At the long
end, a Canon 400mm, f/2.8 lens has a hole that is 143mm across (call it 5.6
inches if you prefer). That's big enough to put your arm through.
Managing the optical paths through such a wide hole is not trivial, but even
more important, when a wide hole and a wide angle of acceptance combine,
the
optical calculations keep supercomputers very busy. Thus the Canon
50mm,f/1.0L is a stunning achievement in "consumer" optics with a 50mm
hole
and an angle of acceptance of 40 degrees. ("Consumer" is relative. This
time, I just mean it doesn't take a government to own one at "only" U$2,500
retail.)
The absolute size of the hole, and the angle of acceptance, are two of the
dominant factors in designing a lens, and meeting that challenge requires
sophisticated manufacturing after inordinately expensive design processes.
That's why you'll find the smallest aperture numbers associated with the
most expensive lenses.
On the other end of the scale, the design challenge of a big hole with a
narrow angle of acceptance is less for something like a prime lens at say
200mm -- but a big hole means a wide lens. That means each element in the
lens is physically larger, requires more high-quality glass (et al), and
more surface area to polish, coat, and so forth. You can plot a neat curve
that will predict the price of a lens and its weight very nicely from the
maximum physical aperture it reaches.
> Therefore shouldn't the lowest aperture (i.e the largest f number)
> be limiting for standard lenses compared to good quality primes?
>
I'm not sure exactly what you mean, but the smallest hole is mechanically
easy to achieve since we just swing the diaphragm blades closer together.
Over quite a range, this just makes the lens' job easier, since the sheave
of paths the light can follow is much narrower. Optical limits do arise at
the smallest holes, but an aperture of say f/16 is easy to manage in the
design and manufacture of a lens. Canon lenses typically provide f/22, and
f/45 is available on the longest lenses (where that is not really a very
small hole in absolute dimensions).
Regards,
Gary W. Sims
Stonehaven Laboratory"
(BTW, I don't really know if I legally have the right to insert such a big quotation. I think it is more convenient than to give a pointer to the EOS mailing list database)
