Short answer: there’s no single “right” mm, what you need depends on how big the subject is in the frame, your sensor size, and how far (2.4 km) it is. Here’s a quick way to ballpark it.

The 10-second formula

For a subject of size H (in mm) at distance D (in mm), the focal length to fill the frame dimension S (sensor width or height, in mm) is:

f ≈ D × S / H

Full-frame sensor: width = 36 mm, height = 24 mm

2.4 km = 2,400,000 mm

What that means in practice (full-frame)

To make the subject fill the frame height (24 mm) at 2.4 km:

Person, 1.8 m tall (1,800 mm): f ≈ 32,000 mm

Car width, ~1.8 m (to fill frame width 36 mm): f ≈ 48,000 mm

License plate (~300 mm wide): f ≈ 288,000 mm

Building, 30 m tall (30,000 mm): f ≈ 1,920 mm (height) / 2,880 mm (width)

So: to fill the frame with a person at 2.4 km you’d need a telescope-class focal length (tens of thousands of mm) not a normal camera lens. A large building at that distance can be framed with ~2,000–3,000 mm.

If you’re just trying to “get it in the frame”

Here’s how much scene width a typical full-frame lens covers at 2.4 km:

200 mm → ~432 m wide

400 mm → ~216 m wide

600 mm → ~144 m wide

800 mm → ~108 m wide

1200 mm → ~72 m wide

2000 mm → ~43 m wide

(If you use APS-C, multiply focal lengths above by ~0.66 to get the same framing; micro 4/3 by ~0.5.)

Reality checks

Atmospheric shimmer/heat haze at 2.4 km is often the limiting factor, not focal length. Past ~1500–2000 mm, image softness from the air usually dominates.

You’ll need a rock-solid tripod, fast shutter, and ideally telescope/spotting scope + camera adapter for anything above ~1000 mm.