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--------------------------------------------------------- By Bill Claff

We'll use lens prescriptions
from .patent (US 6,002,533) to examine how close-up lenses work.

In the patent the close-up lens is presented in the context of a main lens.
Complete details of the main lens are not provided but are easy to determine
with the Optical Bench.

The main lens has a focal length of 100mm and focuses to a reproduction ratio
of 1:2 by extension.

(Even though one lens element moves slightly during focusing this is for close
focus correction and not focusing.)

The lens has an f-number of f/4 and
focused at infinity looks like this:

Take note of the locations of the principal planes.

The close-up lens has three
elements. Three examples are given and we'll examine the first. Then lens looks
like this:

The patent indicates a focal length of 219.711mm and the Optical Bench gets
218.60mm which is pretty much in agreement.

The formula to convert a focal length in mm to diopters (power) is:

*D = 1000mm / f
*1000 / 219.711 ~= 4.55D so this is a 4.55D close-up lens. Take note
that the main lens is 10D (1000mm / 99.98mm).

When we put the two together,
including a 1mm gap between the close-up lens and the main lens at infinity
focus, we get:

The principal planes of the resulting lens lie between those of the component
lenses, closer to the lens with the
higher power (diopters).

The magnification at infinity
focus is 0.455x. This number may look familiar because magnification at
infinity is:

*m = P _{A} / P_{M}*

Where

Magnification at closest focus
is 1.087x which is more than the 0.455x + 0.5x = 0.955x that we might expect.

This is because the drop in focal length acts as additional extension and
because the rear principal plane (H') moved further from the image plane.

Close-up lenses work by reducing
focal length. It's helpful to know the resulting focal length if you are also
going to use extension tubes in conjunction with the close-up lens.

Computing the resulting focal length is widely misunderstood. The formula,
expressed as powers is:

*P = P _{A} + P_{M}
-d_{m * }P_{A * }P_{M}*

Where

Because

In the case of our example lens
we might assume a resulting focal length at infinity focus of 1000mm / (4.55D +
10D) = 68mm

But the result is actually over 79mm because the accessory H to main H'
distance is over 36mm.