A compound microscope consists of an objective lens of focal length 2.0cm and an eyepiece of focal length 6.25cm separated by a distance of 15cm. How far from the objective should an object be placed in order to obtain the final image at (a) the least distance of distinct vision (25cm), and (b) at infinity? What is the magnifying power of the microscope in each case?
Object distance from objective = 2.5 cm; Magnifying power = 20
Object distance from objective = 70/27 cm 2.59 cm; Magnifying power = 13.5
Explanation
This problem involves applying the lens formula to both the objective and eyepiece of a compound microscope. For case (a), when the final image is at the least distance of distinct vision, we first find the object distance for the eyepiece using the lens formula, then determine where the image formed by the objective must be located. For case (b), when the final image is at infinity, the object for the eyepiece must be at its focal point. The magnifying power is calculated as the product of magnifications produced by the objective and eyepiece.