An eye is capable of distinguishing between two points on an object if their separation is greater than 0.22 mm when the object is held 25 cm from the eye. This object is subsequently viewed through a compound microscope that has a 20 D objective and a 10 D eyepiece, separated by a distance of 20 cm . The final image is produced at 25 cm from the eye. Determine the minimum separation between two points of the object

Step-by-step solution

The focal lengths of the objective and eyepiece are given by: f_o = 100 P_o = 100 20 = 5 cm f_e = 100 P_e = 100 10 = 10 cm For the eyepiece, the final image is formed at the near point, so v_e = -25 cm . Using the lens formula: 1 v_e - 1 u_e = 1 f_e 1 -25 - 1 u_e = 1 10 1 u_e = - 1 25 - 1 10 = - 7 50 u_e = - 50 7 cm The distance between the objective and the eyepiece is L = 20 cm . The image distance for the objective is: v_o = L - |u_e| = 20 - 50 7 = 90 7 cm Using the lens formula for the objective: 1 v_o - 1 u_o