@wutsurstyle & RioRico...

Here I use N for f-number to avoid confusion with f for focal length.

The reason for confusion surrounding "effective fnumber" & how/when to use it is that most of the common equations like DOF, exposure, diffraction, shake reduction,

*etc* tacitly assume the lens is one focal length away from the sensor - but for macros it isn't one focal length away - its actual distance is

*always* f(1+m) - meanwhile the diameter of the actual physical aperture has not changed.

*image.distance = focal.length(1+m)* *where m=sensor.width/scene.width*
The m term is usually very small - for a meter wide portrait, m is about 1/40 - that's why it is seldom included in equations intended for normal use..

Unless an equation is specifically written for macro conditions one should substitute f(1+m) for f, and N(1+m) for N for application in macro conditions.

**Common equations including macro conditions:**
Diffraction.spot.diameter = 2.44

*N(1+m)* Wavelength

DoF = 2C

*N(1+m)* /m^2

Relative.light.intensity.at.image = 1/[

*N(1+m)*]^2

Shake.reduction.fnumber =

*N(1+m)* *etc....*
The case for a close-up lens added to a normal lens on a camera is interesting: the close-up lens reduces the focal length of the original lens by a factor of 1/(1+m) and it also increases its fnumber by a factor of (1+m) - these two factors exactly compensate so there is no illumination change when you put on a close-up lens.

Try it! exposure for a particular scene will be the same with and without a close-up lens!

Hope this helps... Sorry for the math but there is no other way.

Dave

PS RioRico said...

*Thus the aperture remains the same. You may see references to EFFECTIVE APERTURE -- and I almost wrote the formula above like that, but it's misleading, like the crap.factor EFFECTIVE FOCAL LENGTH, because the ratio hasn't changed.*

The underlying problem is that focal length is normally used to approximate the distance from lens to image which changes with m.

*The question then is: Given the razor-thin DOF at macro scales, does this make a difference? Is it noticeable?*
It turns out the DOF for close-up lens and extension tube cases are the same

__for the same light intensity on the sensor__.

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Last edited by newarts; 08-02-2011 at 02:26 PM.
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