Geometrical optics. Photometry. Quantum nature of light > Optical systems > Problem 13.3.28

Statement

The microscope has an objective and an eyepiece with a focal length of and , respectively. How much does the magnification of the microscope change if the distance between the objective and the eyepiece is increased by ? How many times will the magnification of the microscope change if all its dimensions, including the size of the lenses, are changed times?

Solution

The total magnification of a microscope is the product of the magnification at the objective , where is the distance between the objective and the eyepiece, and the magnification at the eyepiece ( cm), where cm is the near-point distance of human eyes. Thus, if is increased by , the total magnification will increase by ( cm).

If the microscope is enlarged to times its original size, each of , , will be times its original value (as the radius of curvature of each lens also increases). Consequently, the magnification of the microscope will be times its original value.

Answer

( cm) and times