You are absolutely right - in terms of the lightness or darkness of the
final image there are only two factors: how sensitive the recording media is
and how much light is let into the camera.  The sensitivity of the media
(digital sensor or film) is expressed by the ISO rating, which can be set by
the photographer in the case of digital sensors.  How much light is let in
is the product of the area of the lens opening (aperture) and the length of
time the aperture remains open (shutter speed).

Now, if the photographer is controlling both of these factors manually
(aperture and shutter speed), you are again right that there would be no
need at all for "exposure compensation".  But if you allow the camera to
automatically set these values (as many of us do) for the sake of
convenience, there may be cases where you want the camera to apply an offset
to its normally calculated values in order to compensate for some condition
in the scene (an overall bright scene in which the object of interest is
much darker, a conscious decision to render the scene darker or lighter than
normal to create a special mood, etc.).  For this you have the setting for
"exposure compensation" which is a user selectable amount of offset to the
standard exposure calculation.  You are continuing to allow the camera to
calculate the exposure (so that it will quickly adjust to changing lighting
conditions without input from you), but asking it to modify its normal
exposure to either lighten or darken the final result to suit your creative
vision.  For any given value of exposure compensation the degree of offset
from "normal" stays the same even though the actual exposure values
(aperture and shutter speed) for each frame may vary if the lighting
conditions vary.

Exposure compensation, is really only necessary if you rely heavily on
a camera's exposure meter to determine correct exposure,  and you
encounter an extremely bright scene (lots of snow, light sand, many
people wearing white / pale clothing) or dark scene (night-time, large
expanses of dark colours) , which may cause the light meter to under or
overexpose that scene.
Background: Light meters are usually programmed and calibrated by the
manufacturer to interpret the overall light from a scene as a medium
shade of grey. So when a light meter encounters a predominance of
bright shades or dark shades, it tries to under or over expose them ,
so they become rendered as that medium shade of grey.
If your scene is predominantly a mix of 'medium' colours such as tree
foliage, blue sky, grey fences and telegraph poles, grey bitumen ,
brown rocks, people with a healthy tan complexion, which are all
approximately the same brightness as that medium grey, the exposure
compensation shouldn't be necessary.

When you use exposure compensation, you are sort of ignoring your
camera's suggested exposure, and telling it to momentarily forget what
it has been programmed to do. You tell it to deliberately overexpose
those bright scenes so the whites turn out truly white instead of grey,
and underexpose those dark scenes,  so the blacks turn out truly black
instead of grey.

The exact amount of excess brightness / darkness will determine the
amount of compensation  required.

So you manipulate the camera's recommended exposure by using more
exposure than recommended for very bright scenes, and less exposure
than recommended for very dark scenes.
I don't know exactly how your camera  indicates 'correct', 'under' and
'over' exposure - maybe by flashing lights of zero, plus and minus ?
Or by aligning little pointer bars so they either meet up, or a moving
pointer is above/below a steady pointer.
If the former,  'zero' light means what the camera thinks is 'correct',
plus means the camera thinks the picture is over exposed, minus means
the camera thinks the picture will be under exposed.
In the case of pointer bars, when the pointers are aligned together,
the camera thinks exposure is 'correct', when the movng pointer is
above or to the right of the steady pointer, the camera thinks exposure
is 'over', when the movng pointer is below or to the left of the steady
pointer, the camera thinks exposure is 'under',

Now, what's the difference between aperture ,  compensation, and ISO ?

The aperture inside the camera lens is one of the tools you use to
control the exposure. By increasing the size of the aperture (turning
the aperture settings towards  the numerically smaller numbers : f1.4,
f2,  f2.8, ) or decreasing the aperture size (turning the aperture
settings towards  the numerically larger numbers :  f11, f16,  f22),
you  increase the exposure or decrease the exposure  respectively.

Compensation (explained above) is achieved by (among other things)
changing the aperture setting to increase the exposure to more than
recommended, or decrease the exposure to less than recommended.

In other words, compensation  is the end effect or result, and the
aperture setting is a method of achieving that result.

Compensation can also be achieved by manipulating the camera's ISO
setting, to 'fool' the light meter into believing that you have a
higher or lower ISO  than what's really the case.

So, again, compensation is the effect or result,  and maniuplating the
ISO is another method of achieving that result.

The effect of lowering the ISO is the same  as increasing the aperture
(increasing exposure), and the effect of increasing the ISO is the same
as decreasing the aperture  (decreasing exposure).  Lower ISOs need
more exposure, higher ISOs need less exposure.

Don't know if I've clarified things or further confused you, but that's
my 5c worth of explanation.

regards

daba

You are right. It is most useful in auto-exposure modes to compensate
without switching to manual exposure for under/over-exposures caused
by subject reflectances that are not average (snow, coal-bins are some
extremes...;-)

In thorough form, exposure is a balance between the amount of available

subject light, sensor/film sensitivity (ISO/ASA), lens aperture (f-stop),

and shutter speed. Lower subject light requires a higher sensor/film

sensitivity, and/or a wider aperture, and/or a slower shutter speed.

Sensor sensitivities come in numbers like 50, 100, 200, etc., with each

higher permitting shooting in 1/2 the light level (1/3rd in-between values

also exist). Apertures come in whole values of f1.4, f2, f2.8, f4, f5.6, f8,

f11, f16, f22, f32, etc., and these (with larger numbers) represent 1/2

the light exposure as you move up in value (in-between values exist, and

many lenses with separate aperture rings permit infinitely variable settings

for precise exposure settings). Shutter speeds come in whole values

(in seconds) of 4, 2, 1, 1/2, 1/4, 1/8, 1/15, 1/30, 1/60, 1/125, 1/125,

1/250, etc. (each exposes 1/2 the value of the one before, and many

cameras permit in-between values, especially in some auto modes). The

choices of what to use depend on conditions. Low light requires high

sensor/film sensitivity (400 or so, risking greater noise/grain), and/or a

wide aperture (f2.8 or so, risking little depth of field and so-so lens

performance [the latter is also a problem at stops of f16 and smaller

due to diffraction]), and/or a slow shutter speed (like 1/15, 1/30, etc.,

risking camera shake - most evident at a speed about

1/lens-focal-length=shutterspeed [like for 125mm, figure the shutter

speed should be at or higher than 1/125mm = 1/125th second] or slower).

As a result of the above, many combinations give the same exposure,

like ISO 200, f5.6, and 1/60th second equals ISO 200, f8, and 1/30th

second, which equals ISO 400, f8, and 1/60th a second (for a given

available light level...). Either the shutter speed in Shutter priority mode

(watching for appropriate aperture selection by the camera), or Aperture

in aperture priority mode (watching for appropriate shutter speed

selection by the camera), or Program mode (watching to see that

appropriate values have been selected by the camera - and many

cameras allow you to "slide" the equivalent values to some more to your

liking) can be used under any lighting condition . In addition, many

cameras permit you to bias the exposure toward darker or lighter if you

do not like the average value of the brightness of the pictures you get

from your camera (judged on a reasonably well calibrated monitor).

Personally, I prefer to use "A" mode and occasionally add a bit of

exposure composition - but others prefer other ways of working.

And, the flash on most cameras can be turned off when not needed...

So there...! ;-)

--
David Ruether
DRuether@twcny.rr.com
rpn1@cornell.edu
http://www.ferrario.com/ruether

because I don't

interestingly, you cant change any of these on a disposable 35mm camera
which uses ISO400, and they are still as popular as ever; maybe even
more so.
I guess people got tired of fiddling with the dials and switches and
such and just want to take a photo without having to wait 3 seconds for
the camera to focus.

you could go insane trying to figure out the proper exposure, ISO, etc.
meanwhile aunt Betty will croak and your grandkids will be gettin'
married.