Geometrical (first-order) depth of focus and depth of field — no diffraction or aberrations.
Greivenkamp, Field Guide to Geometrical Optics, pp. 35–36
Depth of Focus & Field (Greivenkamp, pp. 35–36)
Depth of focus (image-plane tolerance):
$$\text{DOF} \approx \pm B'\,f\!/\!\#_W = \pm\frac{B'}{2\,\text{NA}}$$
where $B'$ is the maximum allowable blur diameter at the image plane
Depth of field (object-space range in focus):
$$L_\text{NEAR} \approx \frac{L_O \cdot f \cdot D}{f \cdot D - L_O \cdot B'} \qquad L_\text{FAR} \approx \frac{L_O \cdot f \cdot D}{f \cdot D + L_O \cdot B'}$$
(thin lens, stop at lens; $L_O$ = object distance, $f$ = focal length, $D$ = aperture diameter)
Hyperfocal distance — focus here to have $L_\text{FAR} \to \infty$:
$$L_H = \frac{f \cdot D}{B'} \qquad \Rightarrow \qquad L_\text{NEAR} \approx \frac{L_H}{2}$$
Working F/#: $f\!/\!\#_W = (1-m)\,f\!/\!\#$
Image-space NA: $\text{NA} = \dfrac{1}{2\,f\!/\!\#_W}$