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[Rollei] Suplementary lenses

> Date: Wed, 09 Jan 2002 22:11:50 -0800
> From: Richard Knoppow <dickburk  >
> Subject: [Rollei] Suplementary lenses
> Message-ID: <  >
> References:
>   I think I accidently deleted a post asking about calculating the focal
> length of a lens with a suplimentary lens on it.
>   Suplementary lenses are usually calibrated in diopters. A diopter is the
> reciprocal of the focal length is meters. So, a one diopter lens has a
> focal length of one meter or 39.3 inches. + dioper lenses are postitive or
> converging, - diopter lenses are negative or diverging.
>  The formula for the combined focal length of two lenses is:
> F = f1*f2 / f1 + f2 - d
>   Where f1 and f2 are the focal lengths of the two lenses and d is the
> distance between them.
>   The exact focal length requires knowing the location of the principle
> points but for practical use the distance can be disregarded and the
> formula simplified by leaving out d. For a more exact focal length the
> first principle point can be assumed to be in the space in front of the
> iris diaphragm but the difference will be negligible. For practical
> purposes the diopter value of combined supplimentary lenses adds linearly.

Hi, Richard:

I'm not sure what the question was but I'll supplement your analysis.  lol

If we continue to assume d=0, then the equation reduces to 1/F = 1/f1 +
1/f2, the fundamental equation of thin-lens optics.  We know the focal
length of the body lens, and the focal length of the supplementary lens is
easy to determine: either by specs or just by eye.  The result is that the
resulting overall focal length is less than either one.

The effect on aperture is to decrease the effective aperture by a factor
1/(M+1) where M is the magnification (less than 1 for reduction, greater
than 1 for magnification).  For most single or double element supplementary
lenses, this effect is negligible just as the reduction in focal length is
minor.  We can say that in general f1 >> f2.

Now, if the body lens is focused at infinity and the object is
1-supplementary-lens-focal-length away (from the supplementary lens), we've
got a very elegant model.  After the image is processed by the supplementary
lens, all rays are parallel.  To the body lens, it looks like an object at

Dan Kalish <kaliushkin  >
Flushing, NYC, USA
"I want the quality of Stolichnaya in America to create an image of Russia
that is pure, strong and honest, just like the vodka."  Andrey Skurikhin,
general director of Soyuzplodimport.