Abbe method

The Abbe method (named after Ernst Abbe ) is a measurement method for determining the focal length of a lens as well as its extension to systems of several lenses, in which the position of the main planes is also obtained.

Determination of the focal length of individual lenses according to Abbe

To determine the focal length of a single lens, you need an object (light source and slit), a screen and the lens whose focal length is to be determined. The position of the lens is fixed on an optical bench . The object and the screen are positioned so that a sharp image is obtained. A further focus is made for an object displaced by d . The focal length f zu results from d , the object size G and the two image sizes B and B '

${\displaystyle f={\frac {d}{{\frac {G}{B'}}-{\frac {G}{B}}}}}$

Lens system

Attached to all lenses rigidly to each other on a tab and defining a reference point on this fixed, is obtained by shifting the object and screen to different focus positions three series of measurements of the distance x to the object, the distance x ' to the image and the image size B . To the imaging scale , the following equations result: ${\displaystyle \gamma ={\tfrac {B}{G}}}$

${\displaystyle x=f\left(1+{\frac {1}{\gamma }}\right)+h}$

${\displaystyle x'=f'\left(1+\gamma \right)+h'}$

The parameters h , h ' correspond to the distances between the object or image-side main plane and the reference point. This and the focal length f can be obtained from the measurement series by means of a linear regression . f and f 'often have the same amount but a different sign.

Individual evidence

1. ↑ Patricia Kreuz, THM Physikloaborteam: Determination of the main levels of a lens system. In: https://www.thm.de/mnd/component/edocman/?task=document.viewdoc&id=934&Itemid= . Technische Hochschule Mittelhessen, August 6, 2016, accessed on June 15, 2020 .