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

Step 1. The eyepiece. $m_e = \dfrac{D}{f_e} = \dfrac{25\ \text{cm}}{2.0\ \text{cm}} = 12.5$.

Step 2. The objective. $m_o = \dfrac{|M|}{m_e} = \dfrac{250}{12.5} = 20$.

Step 3. Its focal length. $m_o = \dfrac{L}{f_o}$. We want $f_o$, so $f_o = \dfrac{L}{m_o} = \dfrac{16\ \text{cm}}{20} = 0.80\ \text{cm}$.

Step 4. The lenses. The distance is $f_o + L + f_e = 0.80\ \text{cm} + 16\ \text{cm} + 2.0\ \text{cm} = 18.8\ \text{cm}$.