综合考虑了透镜的焦深、厚度、球差等因素,对高斯公式法(实物成实像法)测量凸透镜焦距的不确定度进行了较全面的分析,并提出了校正由透镜厚度及球差引起的系统测量偏差的方法。对于选定的标称焦距为25.0 mm的凸透镜,其测量不确定度随着物距的增大先减小后增大,校正前最小值为1.26 mm,其中透镜球差的存在对于测量不确定度的影响最为突出。系统测量偏差校正后,其不确定度变化趋势不变,最小值降低为0.10 mm,这大大提高了测量结果的准确度。不确定度分析结果表明将物点置于透镜的二倍焦距附近得到的测量结果更为可靠,所得结果为实验操作提供指导依据。

In this paper, the uncertainty of convex lens focal length measured based on the Gauss formula method (real object-real image method) is analyzed comprehensively considering the factors of the depth of field, thickness, and spherical aberration of the lens, and a method to correct the systemic measurement deviation caused by lens thickness and spherical aberration is proposed. For the selected convex lenses with a nominal focal length of 25.0 mm, the measurement uncertainty decreases first and increases afterward with the increase of the object distance, and the minimum value before correction is 1.26 mm, where the spherical aberration of the lens has the most prominent influence on the measurement uncertainty. After the system measurement deviation being corrected, the change trend of the measurement uncertainty remains unchanged and the minimum value is reduced to 0.10 mm, which indicates that the deviation correction improves the accuracy of the measurement results greatly. The results of uncertainty analysis show that the measurement results are more reliable when the object point is placed near the twice focal length of the lens, providing a guide for experimental operation.