The measurement of the focal length of a bi-convex lens using auto-collimation imaging is a fundamental experiment in college. However, some teachers and students are confused by unwanted reflection images unaffected by the plane mirror when tracking the accurate image reflected by that mirror. By delving into the formulas of the reflection imaging of thin lenses through two different reflection imaging methods and introducing the notion of focal power, this paper obtained the inequalities determining the formation of the reflection images. These inequalities can explain the existence of the reflection images, analyze the general cases of reflection imaging using a thin lens, and do a quantitative calculation of a thin lens with specific parameters. This work can help teachers and students understand the reflection imaging of thin lenses, and it can be designed as an experimental procedure to foster greater scientific interest among students in this subject by combining different teaching methods.