Hi!
To understand how a close-up lens works, I prefer thinking in terms of images instead of thinking in terms of changed focal length or modified optical system.
A close-up lens is a single positive lens element with a given focal length "f", e.g., 1 meter, f = 1m.
Suffice to consider the object-image correspondence in a single lens element.
If the subject, e.g. a flower, a butterfly or a mushroom, is located at a distance of one meter (generally speaking = one focal length) in front of this close-up lens, by definition of the focal point, the image delivered by the close-up lens is located at infinity.
The camera's taking lens set-up for infinity, sees this image at infinity and eventually delivers a sharp image in its own focal point, since the new "object" (actually: the image delivered bu the close-up lens) is located at infinity.
A close up lens with f=1m brings the image of an object located at a distance of one meter to infinity.
A close up lens with f=0.5m brings the image of an object located at a distance of 0.5m = 50 cm to infinity.
A close up lens with f=0.33m = 1/3 m brings the image of an object located at a distance of 33 cm to infinity.
Hence, no need to compute the equivalent focal length of the combined optical system (close-up lens + camera lens).
Now a more subtle issue is: with a close-up lens, do I need an exposure correction?
The answer is simply: no, with a close-up lens added in front of the camera's taking lens, no exposure compensation or correction is needed.
(the reason is a bit difficult to explain, but will be explained here in detail, with pleasure, upon request )
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