Question

A microscope has a $20cm$tube length. What focal-length objective will give total magnification localid="1649845070556" $500\times$when used with an eyepiece having a focal length $5.0cm$?

Short answer

The objective will give a total magnification $500\times$is $0.2cm$.

Step-by-step solution

Given Information.

We have given that:

Tube length$L=20cm$,

Magnification localid="1649845198764" $M=500\times$

Focal length $f_{eye}=5cm$

We need to find the focal length.

Simplification.

As we know a total magnification microscope:

$$\begin{gathered} M=-\frac{L}{f_{obj}}\times \frac{25}{f_{eye}} \\ 500=\frac{20}{f_{obj}}\times \frac{25}{5} \\ 500=\frac{20}{f_{obj}}\times 5 \\ 500=\frac{100}{f_{obj}} \\ {f}_{obj}=\frac{100}{500} \\ {f}_{obj}=0.2cm \end{gathered}$$

Here $f_{obj}$is the focal length of an object and $M$is magnification.