This study focuses on the optical system of achromatic objectives for refracting telescopes. The focal length of a convex lens is measured using the parallel light method, and its refractive index is determined via the thick lens formula. By measuring the focal length of a compound lens composed of convex and concave lenses, the focal length of the concave lens is deduced, enabling the determination of its refractive index. Based on the achromatic condition formula, the lens materials and Abbe numbers are derived, validating the design principles of achromatic compound lenses.