We find a final separation distance of is (0.0045 ± 0.0005) m. From Equations 8 and 11, we find that the magnification factor is 0.50±0.06. The magnification factors of the two set-ups are inverses since the first set-up doubles the separation and the second halves it. This is expected since we reversed the order of the lenses. The goal of the second part of the lab was to find the focal lengths and dioptric powers of various lenses. After measuring the focal lengths, we calculated the dioptric powers of the lenses using the fact that the dioptric power, P, is the inverse of the focal length. The uncertainties for the calculations in Table 2 were found using the following equation:
δP=P_best δf/f
where P_best is the calculated dioptric power, f is the focal length, δf is the uncertainty of the focal length. The fourth row of Table 2 contains the data relevant to the combination of the two thin lenses (3.5 cm diameter and 4.0 cm diameter). The theoretical dioptric power of the two thin lenses together is given by the following