A student builds a compound microscope. The eyepiece has a focal length of 2.0 cm…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A student builds a compound microscope. The eyepiece has a focal length of $2.0\ \text{cm}$ . The distance between the second focus of the objective and the first focus of the eyepiece is $16\ \text{cm}$ . She wants a total magnifying power of magnitude $250$ , with the final image at infinity. Find the focal length of the objective, its magnifying power, and the distance between the two lenses.

Need a reminder? The key ideaShow

Simple microscope: $m = 1 + \dfrac{D}{f}$ (image at the near point) and $m = \dfrac{D}{f}$ (image at infinity), with $D = 25\ \text{cm}$ . Compound microscope: $M = m_om_e$ , with $m_o = \dfrac{v_o}{u_o}$ . For the final image at infinity, $M = -\dfrac{L}{f_o}\cdot\dfrac{D}{f_e}$ and the lenses are $f_o + L + f_e$ apart.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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