Image processing for quantitative measurement of e/m in the undergraduate laboratory

Abstract

Abstract In conventional e/m experiments performed in undergraduate laboratories, generally a simple mechanical ruler is used to measure the radius of the circular trajectory of the electrons. But, the measurement error in this technique is mostly big and varies from one student to another. As an alternative to a mechanical ruler, we proposed a more accurate and a more precise technique for measuring the radius. This technique is based on image processing and it is well known that the image processing is one of the more powerful techniques for precise measurements in physical experiments. ImageJ software was used for image processing and for taking photographs of the circular trajectory of the electrons in the e/m experiment. ImageJ is a java-based image processing program which was developed by the National Institute of Health of USA. The photographs of the trajectory were taken by using a generic webcam connected to the computer and it was observed that the trajectory was not visible for a one shot photograph which is due to the low intensity of the light coming from the trajectory. By taking multiple photographs of the trajectory at the same time and adding these photographs to each other, the trajectory on the photograph became visible. It was concluded that the accuracy of the measuring the radius of the circular trajectory could be increased by using the image processing and it was found that the relative error made in this measurement is about 0.5% which is 10 times smaller than the relative errors made in conventional measuring techniques performed by a simple mechanical ruler (around 5%). This result directly increases the precision and the accuracy of measuring the e/m ratio of the electrons in undergraduate physics laboratories.