What is Compound microscope?

Example 4.12 (A student microscope)

Objective $f_1' = 4.0\,\mathrm{mm}$, eyepiece $f_2' = 25\,\mathrm{mm}$, $\Delta = 160\,\mathrm{mm}$: $\gamma_1 = -40$, $G_2 = 10$, $G = 400$. The object sits at $\overline{F_1A} = -f_1'^2/\Delta = -16/160 = -0.10\,\mathrm{mm}$ from $F_1$: $4.1\,\mathrm{mm}$ from the objective. Focusing means moving the whole tube by fractions of a millimeter.

Example 4.9 (A watchmaker’s loupe)

$f' = 25\,\mathrm{mm}$: $G = 250/25 = 10$, sold as “$10\times$”. A $0.05\,\mathrm{mm}$ detail then subtends $2 \times 10^{-3}\,\mathrm{rad}$, comfortably resolved. Pushing $G$ higher means $f'$ of a few millimeters, a tiny lens held against the eye — the limit of the single lens, and the reason the microscope exists.

Example 4.16 (An amateur’s 150-millimeter refractor)

$D = 150\,\mathrm{mm}$, $f_1' = 1200\,\mathrm{mm}$, eyepiece $25\,\mathrm{mm}$: $G = -48$; exit pupil $3.1\,\mathrm{mm}$; light gain $(150/7)^2 \approx 460$ against a dark-adapted pupil of $7\,\mathrm{mm}$; resolution $1.22 \times 550\,\mathrm{nm}/0.15\,\mathrm{m} = 4.5 \times 10^{-6}\,\mathrm{rad} = 0.9''$, so craters $1.7\,\mathrm{km}$ wide on the Moon; $G_r = 3\times10^{-4}/4.5\times 10^{-6} \approx 67$ — the $6\,\mathrm{mm}$ eyepiece ($G = 200$) shows no more detail, only a dimmer, bigger disk. The weekend problem designs this instrument.