Focal Length

The mm number you see on a lens — "50mm", "200mm". Length, yes, but not the distance between lens and sensor in general.

Strict definition

The distance from the lens's optical center (principal point) to the plane where the image forms (sensor), when focused at infinity.

Focusing on a closer subject actually pushes this distance longer. So the "lens-to-sensor distance" intuition is half right, half wrong.

Why bigger mm = farther reach

Longer focal length narrows the angle of view projected onto the same sensor. Spreading a narrower angle across the whole sensor produces magnification.

Short focal length (wide):  ━━━━━ wide area, captured small
Long focal length (tele):    ─    narrow area, captured large

Why 50mm is "standard"

The intuition that it's "close to human vision" is roughly right.

• A full-frame sensor (36×24mm) has a diagonal of about 43mm. Focal lengths near this number give the most natural-feeling perspective relative to human sight.
• A 43mm lens is awkward to make, so 50mm became the de facto standard.
• The full binocular field of view is around 200°, but the attentive central area is only 40–50°. 50mm matches the latter.

Angle of view also depends on sensor size

The same 50mm lens gives a narrower angle on a smaller sensor. See crop-factor.

Related

• lens-basics — Parent note
• crop-factor
• depth-of-field
• perspective-compression
• exposure-triangle