13.3.28. The microscope has an objective and an eyepiece with a focal length of $f_1$ and $f_2$, respectively. How much does the magnification of the microscope change if the distance between the objective and the eyepiece is increased by $l$? How many times will the magnification of the microscope change if all its dimensions, including the size of the lenses, are changed $k$ times?
Solution
The total magnification of a microscope is the product of the magnification at the objective $L/f_1$, where $L$ is the distance between the objective and the eyepiece, and the magnification at the eyepiece ($25$ cm)$/f_2$, where $25$ cm is the near-point distance of human eyes. Thus, if $L$ is increased by $l$, the total magnification will increase by ($25$ cm)$\cdot l/(f_1f_2)$.
If the microscope is enlarged to $k$ times its original size, each of $L$,$f_1$,$f_2$ will be $k$ times its original value (as the radius of curvature of each lens also increases). Consequently, the magnification of the microscope will be $1/k$ times its original value.