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I really like a deeply washed out background as a backdrop. I expect using a 35mm film camera that f-stops is inversely related to depth of field. I assume this remains true for compound lenses. But now that there is a wide range of sensor sizes I'm not clear when I look at a lens what to anticipate for the depth of field.

How can I know what to expect for the depth of a field of a lens for a given sensor size? As part of that, is it true that depth of field is inversely related to f-stops, even for a compound lens?

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Try a DoF calculator like DoFMaster: http://www.dofmaster.com/dofjs.html

Not sure what you mean by "compound lens"—zoom maybe? lens+converter?—but yes, DoF is always inversely proportional to f-stop.

DoF is also inversely proportional to magnification.

DoF might be inversely proportional to lens focal length if you hold subject distance constant. But if you hold magnification constant then DoF is not affected by focal length/field of view. Except with different fields of view you can't hold magnification constant everywhere. When dissimilar lenses have the same magnification at subject plane they do NOT have the same magnification at infinity.

Confused yet?

You end up with a hard-to-wrap-your-head-around idea called equivalence:

http://www.josephjamesphotography.com/equivalence/#quick

Good luck.

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If you are comparing lenses / cameras with roughly equal field of view then the quantity you want to look at to determine the level of background blur is the diameter of the entrance pupil.

This is easily calculated from the spec sheet by dividing the focal length by the f-number. For a 100mm f/2.0 lens the entrance pupil is 100/2 = 50mm wide.

A 25mm f/2.0 lens on a micro 43rds size sensor has a 12.5mm entrance pupil. A 50mm f/2.8 lens on full frame has a 17.9mm entrance pupil and will thus give a more blurred background. In fact the diameter of the background blur will be directly proportional to the entrance pupil diameter.

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