Determine the maximum magnifying power of a compound microscope equipped with a 25 diopter lens as the objective and a 5 diopter lens as the eyepiece, given a separation of 30 cm between the two lenses. The least distance for clear vision is 25 cm .

Step-by-step solution

Focal length of objective lens, f_o = 100 P_o = 100 25 = 4 cm Focal length of eyepiece lens, f_e = 100 P_e = 100 5 = 20 cm For maximum magnifying power, the final image is formed at the least distance of clear vision, v_e = -25 cm . Using the lens formula for the eyepiece: 1 v_e - 1 u_e = 1 f_e 1 -25 - 1 u_e = 1 20 1 u_e = - 1 25 - 1 20 = - 9 100 |u_e| = 100 9 cm The separation between the lenses is L = v_o + |u_e| = 30 cm . v_o = 30 - 100 9 = 170 9 cm Using the lens formula for the objective: 1 v_o - 1 u_o = 1 f_o