LENS
APERTURE
To
obtain an exposure, a lens must be controlled through its aperture,
just like the iris of the human eye. "In bright-light
situations, the iris is dilated to reduce the size of the pupil
and limit the amount of light which enters the eye; and in dim-light
situations, the iris adjusts its size so as to maximize the
size of the pupil and increase the amount of light which enters
the eye"2
F-STOP
The
lens aperture controls the amount of light it transmits
to the
film or sensor plane, by adjusting the size of the opening
in the lens diaphragm. The relative size of such aperture
openings
is represented by f-numbers, called apertures or f-stops.
The
actual diameter of the aperture can be calculated by dividing
the focal length over the f-stop value. The apertures are shown
below for a 50mm f/1.4 Nikkor lens, as well as the actual diameters
of each one.
The
f-stop numbers follow a rounding figure convention for the sake
of engraving aperture rings, now useful in LCD displays. Since
each full f-stop number was established to progressively allow
for twice as much light transmission as the next larger one,
true f-stop values are multiples of the square root of 2 or
1.4142 as follows:
nominal |
f/1.4 |
f/2 |
f/2.8 |
f/4 |
f/5.6 |
f/8 |
f/11 |
f/16 |
f/22 |
f/32 |
| true |
1.4142 |
2.0000 |
2.8284 |
4.0000 |
5.6568 |
8.0000 |
11.3137 |
16.0000 |
22.6274 |
32.0000 |
To
illustrate what the apertures really mean for light transmission,
lets imagine a situation where 100% of light would be transmitted
at f/4:
| f/stop |
f/1.4 |
f/2 |
f/2.8 |
f/4 |
f/5.6 |
f/8 |
f/11 |
f/16 |
f/22 |
f/32 |
| % |
800% |
400% |
200% |
100% |
50% |
25% |
12.5% |
6.25% |
3.125% |
1.5625% |
F-STOP AND SHUTTER SPEED
How
long we let such transmitted light hit the film or sensor is
the second control variable for exposure: shutter speed. The
following table shows equivalent exposures, as combinations
of f-stop values and shutter speeds in fractions of a second,
considering a sensitivity of ISO 100 under bright light conditions
in open shade:
| f/stop |
f/1.4 |
f/2 |
f/2.8 |
f/4 |
f/5.6 |
f/8 |
f/11 |
f/16 |
f/22 |
f/32 |
| shutter |
1/8000 |
1/4000 |
1/2000 |
1/1000 |
1/500 |
1/250 |
1/125 |
1/60 |
1/30 |
1/15 |
What
is important of the exercise above is that: for a given exposure,
each one more full stop "down" (smaller in diameter)
requires twice longer the shutter speed of the previous one.
For each one more full stop "up" (bigger in diameter)
to achieve the same exposure requires half longer the shutter
speed than the stop before.
F-STOP,
SIZE OF GLASS AND COST
The
wider the aperture of a lens is, the faster it can
shoot when
wide open (at its smallest f/stop number), the larger the glass,
the higher its materials and manufacturing costs and
therefore
its price. For available dim light photography a "fast" lens
is required.
How
wide is widest possible depends on the focal length
and the
complexities and feasibility of manufacturing such lens. A
50mm f/1.8 lens has an effective diaphragm aperture
of 50mm/1.8 =
27.8 mm (1.1") of diameter; a more manageable size than that
of a 600mm f/4 that has a diameter of 150 mm (5.9"). This lens,
to be a f/1.8 would need an effective diaphragm aperture of
600/1.8 = 333 mm (12.1"), a very wealthy person to order it
and one strong pack mule or two to carry it.
A
lens is known as a "pro" lens when it is "fast", has
been corrected for all kinds of possible aberrations
and it is built to last a lifetime, provided we don't drop it.
2
The
Physics classroom. Lesson 6. The Eye
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