A compound microscope is composed of an objective with a focal length of 1 cm and an eyepiece with a focal length of 5 cm . An object is positioned 0.5 cm from the objective. Determine the separation between the lenses required for the microscope to project an inverted real image of the object onto a screen located 30 cm behind the eyepiece.

Step-by-step solution

Using the lens formula for the objective lens: 1 v_o - 1 u_o = 1 f_o Substituting u_o = -0.5 cm and f_o = 1 cm : 1 v_o - 1 -0.5 = 1 1 1 v_o + 2 = 1 1 v_o = -1 v_o = -1 cm The image formed by the objective is virtual and is located 1 cm in front of the objective. For the eyepiece, the final image is real and is formed on a screen 30 cm behind it. Using the lens formula for the eyepiece: 1 v_e - 1 u_e = 1 f_e Substituting v_e = 30 cm and f_e = 5 cm : 1 30 - 1 u_e = 1 5 1 u_e = 1 30 - 1 5 = 1 - 6 30 = - 5 30 = - 1 6 u