What is Real and virtual images?

Example 10.10 (The formula at work)

An object stands $30\,\mathrm{cm}$ in front of a converging lens with $f' = 10\,\mathrm{cm}$: $\overline{OA} = -30\,\mathrm{cm}$, so

a real image $15\,\mathrm{cm}$ behind the lens, inverted, half-size — exactly what the three rays draw.

Example 10.14 (Prescribing for a myope)

A myopic eye has its far point at $50\,\mathrm{cm}$: the correcting lens must show distant objects at the far point — object at infinity, image at $\overline{OA'} = -0.50\,\mathrm{m}$ (virtual, in front). Then $1/f' = 1/\overline{OA'}$: $f' = -0.50\,\mathrm{m}$, $C = -2.0$ D; the relaxed eye looks at that virtual image and sees it sharply.

Example 10.16 (A jeweler’s loupe)

Loupe with $f' = 5.0\,\mathrm{cm}$, stone at $4.0\,\mathrm{cm}$: $1/\overline{OA'} = 1/5.0 - 1/4.0 = -1/20$, so $\overline{OA'} = -20\,\mathrm{cm}$ and $\gamma = (-20)/(-4.0) = +5.0$: a virtual, upright image, five times larger, a comfortable $20\,\mathrm{cm}$ from the lens.