A compound microscope has an objective lens of focal length $f_o=3\text{mm}$ and an eyepiece of focal length $f_e=20\text{mm}$. The tube length (distance between the lenses) is $L=150\text{mm}$ and the final image is formed at the near point of a relaxed eye ($D=25\text{cm}$). Calculate the overall linear magnification $M_{\text{total}}$ of the microscope.

Step-by-step solution

1. Convert all lengths to the same unit (millimetre). $D=25\text{cm}=250\text{mm}$.
2. For a microscope adjusted for relaxed eye, the overall magnification is $M_{\text{total}}=\frac{D}{f_e}\times \frac{L}{f_o}$.
3. Compute the first factor: $\frac{D}{f_e}=\frac{250}{20}=12.5$.
4. Compute the second factor: $\frac{L}{f_o}=\frac{150}{3}=50$.
5. Multiply the two factors: $M_{\text{total}}=12.5\times 50=625=6.25\times 10^2$.

Concept tested: Overall magnification of a microscope

Published 14 September 2026 · How this solution was prepared and checked