Calculating the focal length of a concave mirror computerically using mathematical algorithms using MATLAB

Abstract

This study proposes the use of digital image processing technology to determine the focal lengths of simple concave mirror , as well as spherical mirrors. This method is simpler, faster to implement, and more accurate in calculating the focal length by taking several pictures at different distances for the image formed by the lens, then calculating the least point spread function for these pictures at that distance to determine the best image. In this work Image No. (7) represents the image that carries the least (psf) that was determined by algorithms and special mathematical equations through the (Matlab) program, then the focal length is calculated by employing algorithms and mathematical equations specific to calculating the focal length. A comparison was made with the traditional method by taking measurements of a group of students at the Optics laboratory of University of Wasit, College of Science (which depends on view to choose the best image). This method has proven to be superior in measuring the focal length of lenses. A statistical analysis was conducted for these measurements for the group of students and it was found that there was differences measurements with an error rate, which confirms the feasibility of this method in terms of measurement accuracy and time saving. Experimental results have confirmed this.

Keywords

• focal length . concave mirror. digital image