The more interesting question is what does the "multiplier" do to
the depth of field.
Put your 200mm lens on a 35mm film camera, frame, take your
shot. Now pick up your camera and lens, and move backwards
away from your subject for a few steps until your subject
now only occupies about 63% of frame, re-focus, and take
a second shot with the same aperture. For the second shot,
"crop" the resulting image to match the first shot's
framing. Print both images.
Both shots have the same composition, of course (though
the second shot will have flatter perspective due to the
increased distance from the subject). The second
shot is enlarged more than the first, for film you'll see
greater grain. You'll find that the second shot has greater
depth of field than the first.
Why? Depth of field depends on lens focal length, distance
from the subject, aperture, amount of enlargement to desired
print size, and the desired resolution of that final print.
When you "move back and re-crop", you're changing distance
and enlargement. Increasing the distance increases depth of
field, increasing enlargement decreases depth of field,
but these changes don't cancel each other out because changes
in distance effect depth of field at a greater rate
(exponentially) than changes in enlargement (linearly),
so the net effect is greater depth of field.
If after taking the first shot you remain in the same
position and put your 200mm lens on a D60 you're going to
find that the subject no longer fits in the frame. If you
then keep stepping backwards until you recover the framing
of the first shot, you'll find you're in the same position
you were in for the second shot above. The image projected
by the lens onto the "insides" of the D60 now looks exactly
the same as the image inside the film camera looked for that
second shot above, but the D60 sensor covers only the center
of that projected image, not quite reaching the edges,
effectively cropping them out. If you re-focus and take an
exposure with the D60, you'll get comparable results to the
second film shot above, with identical framing and identical
depth of field (and identical perspective). Recall that this shot
had identical framing but greater depth of field and flatter
perspective than the first film shot.
Note that the "other way" of using a D60 to take the
same composition is to stay the same distance as the first film shot,
and use a 125mm focal length on a D60. Your framing will be
the same, and if you use the same aperture you'll find your
depth of field is yet again slightly greater than in the
first film shot. Here you've decreased the focal length of
the lens (which increases depth of field) while increasing
the enlargement factor (which decreases depth of field).
Similar to the earlier D60 case, changes to focal length
impact depth of field at a higher rate (exponentially)
than changes in enlargement do (linearly), so the effects
don't cancel each other out, instead they lead to a greater
depth of field. Also, by maintaining your distance to the
subject, this time you'll capture the same perspective
as the first film shot above (less flat than the shots made
further away).
The short answer is that if you want to calculate depth
of field, you need to choose a circle of confusion that's
derived directly from your enlargement factor (the ratio
between your sensor size and your target print size) and
your desired resolution on that print (i.e. 5-10 lp/mm).
Whatever number you'd use on a 35mm film camera, you should
divide that number by 1.6 on a D60 to compensate for the
additional enlargement. Then use a depth of field calculator
with that circle of confusion and the "real" focal length
of the lens (not multiplied by 1.6).
-harry
