Magnification of Compound Microscope

From the ray diagram, the linear magnification produced by the objective alone is $m_o=h'/h$; using the tube length $L$ (the distance between the objective's second focal point and the eyepiece's first focal point) and $\tan\beta=h/f_o=h'/L$, this simplifies to $\boxed{m_o=L/f_o}$. Combining this with the eyepiece's own simple-microscope magnification -- $m_e=1+D/f_e$ for near point focusing, or $m_e=D/f_e$ for normal focusing -- gives the compound microscope's total magnification: $\boxed{m=m_o, m_e=\dfrac{L}{f_o}\left(1+\dfrac{D}{f_e}\right …