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Macro Lens Calculations

Trying to work out which lens in my collection is best for macro photography with extension tubes. Rather than try them I thought I’d see if I could calculate the answer. Then potentially use this to work out which lens to buy next.

There are other methods to use non-macro lenses for macro photography however in this article I’m just considering Extension tubes.

Terms

The following are the terms used in the calculations:

f = Focal Length

The measure of how a lens converges / diverges light.

U = subject distance

Distance from the subject to a point in the lens. This is not the same a MFD.

V = Image distance

Distance from the projected image to the to a point in the lens. This is not necessarily the same point U and depends on lens design.

Mag = Magnification of lens

To be considered “macro” this needs to be 1 or greater.

LT = Length of Extension tube

The physical length of the extension tube / tubes from flange to flange.

MagT = Magnification of lens & Extension tube

Magnification once a given length of extension tube has been applied to a given lens.

I = Image Size

Size of the image projected on to the sensor of the camera

S = Subject Size

Size of the subject the camera is pointing at.

MFD = Minimum Focus Distance

Minimum distance the subject can be from the lens, not the same as U / subject distance.

Formulas

Focal Length:

1 / f = ( 1 / U ) + ( 1 / V )

Magnification:

Mag = V / U

Magnification after adding an extension tube:

( LT / f ) + Mag= MagT

Image size:

I = Mag x S

Conclusion

Fundamentally the smallest focal length lens will always win however minimum focus distance may also have a factor here.

For my 35mm sensor camera I can obtain a magnification factor of just over 1 using my 24mm and 28mm lenses with 26mm of extension tubes.

For my APS-C sensor camera I can obtain a factor of just over 1 with a 16mm lens and a 16mm extension tube. If however I use 26mm of tubes I can get a factor of around 1.7.

Of course 1.7 sounds better than 1 however it needs to be as a 35mm sensor is 1.5 times bigger than an APS-C. Also for a given number of pixels the 35mm sensor will have bigger pixels so will be less prone to noise.

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