Question #43565

Two thin convex lenses are to be placed in contact to form a combination. To determine their individual focal lengths, each lens is placed exactly at the zero mark of an optical bench, and the coordinate of its principal focus is measured. The measured coordinates of the foci for the two lenses are $x_1 = 25.2 \text{ cm}$ and $x_2 = 12.7 \text{ cm}$. The optical bench scale has a least count of $0.1 \text{ cm}$ and a positive zero error of $+0.2 \text{ cm}$ (i.e., the scale reads $0.2 \text{ cm}$ when the actual distance is zero). The zero error was determined by a single measurement using the same scale. Assuming the placement of the lenses at the zero mark introduces no additional uncertainty, calculate the power of the lens combination and its maximum absolute uncertainty.