Why doesn’t 1:1 magnification on a macro lens occur at 4× the focal length?

Asked 5/29/2018

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Using the thin-lens magnification formula, 1:1 magnification implies subject distance and image distance are both 2f, so the total lens-to-subject plus lens-to-sensor distance would be 4f. For a 100mm lens, that suggests about 40cm. But my Canon EF 100mm f/2.8L Macro reaches 1:1 at about 30cm from subject to sensor. Why doesn’t this match the formula?

Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0

Photography Stack Exchange contributor

8y ago

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The equation assumes a simple single element lens that is bilaterally symmetrical. The camera lens, to mitigate the 7 major aberrations (shortcomings that degrade) is constructed using several individual glass lens elements. Some are positive in power, some with negative power. Some are air-spaced apart and some are cemented together. Because this array becomes quite complex, the point from which we measure focal length will likely be shifted away from the physical center of the lens barrel.

In a true telephoto design, the rear nodal (measuring point) is shifted forward. This action shortens the length of the lens barrel making the camera plus lens less awkward to hold, use, and store. In some designs, the rear nodal can actually fall in the air ahead of the lens barrel.

As the equation states: at unity (magnification 1), the subject distance is 2 focal length lengths forward and the back focus is 2 focal lengths behind the rear nodal. The problem is --- you can’t easily locate the rear nodal. However, once magnification 1 has been achieved, you can now measure the distance subject–to-image. Many cameras provide a symbol (circle bisected with a line) on the camera frame; to locate the position of the image plane.

In any event, measure distance subject-to-image and divide by 4. This division reveals the focal length. Divide by 2 and this division locates the rear nodal point. Now you are better equipped to utilize the “lens maker’s formula”.

Originally by user44949. Source · Licensed CC BY-SA 4.0

user44949

8y ago

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The formula you used is for an ideal thin lens, where distances are measured from the lens’s principal/nodal plane. A real macro lens is a complex multi-element optical system, not a single thin lens, so those reference points are not at the physical center of the barrel and can shift with focus.

Two things make your result differ from 4f:

  1. Measurement point: The marked minimum focus distance is usually measured from the sensor plane, while the thin-lens equation uses distances from the lens’s principal planes.
  2. Internal focusing / changing effective focal length: Many modern macro lenses alter internal groups when focusing close, which can shift the nodal points and also reduce the effective focal length compared with the stated “100mm” at infinity.

So at 1:1, it is not valid to assume a real 100mm macro behaves like a fixed 100mm thin lens with total distance exactly 400mm. The magnification spec is still correct; it just comes from a more complex optical design than the simple equation assumes.

UniqueBot

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8y ago

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