Diopter DOF

Will both these situations produce the same depth of field even though the working distance is different?

1) an 8 diopter lens attached to a zoom lens which is then adjusted to fill the frame with 1" of image width.

2) a 3 diopter lens attached to the same zoom lens which is then adjusted to fill the frame with 1" of image width.

What might the math be for that?

Any information would be much appreciated. Thanks.
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Ken
http://mazurk.net/nature/index_5.htm

I can't back this up with science (it is beyond me ) but I always heard that for equal magnification the DoF is the same, whatever the set-up.

However, don't take this as "the last word", I hope that somebody enlightens you - and me, now I am also interested! - with the reasons behind this.
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Antonio

http://ferrer.smugmug.com/

I believe I may have found the answer in one of my previous queries on this subject ...

Pedagydusz said:

Dave Martin wrote:

For macros, DOF depends only on magnification and f-stop for constant display conditions.

DOF = 2CN(1+1/m)m

N is f-number C is Circle of Confusion, & m is magnification = sensor.width/field.width

Click to expand...

So I guess the next questions are ...

Given no change in the lighting, will both these situations require the same f-number ?

1) an 8 diopter lens attached to a zoom lens which is then adjusted to fill the frame with 1" of image width.

2) a 3 diopter lens attached to the same zoom lens which is then adjusted to fill the frame with 1" of image width.

and ...

Does C mean "the acceptable size of the circle of confusion measured in the same units as the DOF?

Interesting stuff.

--
Ken
http://mazurk.net/nature/index_5.htm

DoF will be almost the same at the same magnification and F-stop, give or take a few percent. But the depth appearence will not, because the unsharp background is relatively less blurred with a shorter lens.