The length of the compound microscope is 15 cm . The magnifying power for relaxed eye is 25 . If the focal length of eye lens is 6 cm then the object distance for objective lens will be

Step-by-step solution

Given parameters: microscope length L = 15 cm , magnifying power M = 25 , eyepiece focal length f_e = 6 cm , and standard least distance of distinct vision D = 25 cm . For a relaxed eye with final image at infinity, the objective image forms at the eyepiece focal point. Thus, the objective image distance is determined by v_o = L - f_e = 15 - 6 = 9 cm . The magnifying power formula yields M = ( v_o u_o ) ( D f_e ) . Substituting known values gives 25 = ( 9 u_o ) ( 25 6 ) . Solving for the object distance u_o results