Bessle and Abbe

I. Introduction

The focal length of a lens in an optical system measures how strongly the system converges or diverges light. There are several methods in which the focal length of a lens can be determined. One method for determining the focal length was developed by Bessel's method which utilizes and object and a screen separated by a distance, L, where L is four times larger than the actual focal length. It is then possible to place the lens at either of the two locations, both between the object and the screen, so an image is then projected onto the screen. Bessel's method utilizes two distances, to create two images, the difference between the two distances are defined as D and is used in the derived equation:

f=((L^2-D^2))/4L

Another method of determining the focal length of a lens was developed by Abbe. The method Abbe developed left the lens in a fixed position and moved the object and the screen to create an image on the screen, the magnification of the two images are calculated through the equation of magnification:

M=h^'/h

Where the object and image heights are used to determine the magnification. The object distance and magnification are utilized in the Abbe's equation for calculating the focal length of the lens:

f=((s_2-s_1))/((1/M_1 -1/M_2 ))

II. Procedure

The two methods for determining the focal length of a lens were performed for 3 separate lenses. Bessel's method was recreated using a lens with a known focal length, utilizing and optical bench, object, and screen to calculate the various distances by moving the lens until an image appeared at two different distances on the optical bench. The focal length was then calculated using Bessel's equation for determining the focal length. Abbe's method was recreated using a lens of known focal length, however the lens was kept at a fixed position and the object and the screen were moved to until two images at two separate distances were observed. The magnification of the two images were calculated and the distances were used to calculate the focal length of the lens using Abbe's method.

III. Results & Discussion

Table 1: Results of Bessel's Method

Lens Focal Length Calculated Focal Length Percent Error

1 100mm 100.32mm 0.32%

2 150mm 147.7mm 1.52%

3 50mm 54.9mm 9.8%

Calculations of the focal lengths can be viewed on the attached data sheets.

Table 2: Results of Abbe's Method

Lens Focal Length Calculated Focal Length Percent Error

1 300mm 256mm 14.7%