There isn't a single fixed distance at which visible light "stops" being observable. In principle, visible light can travel across the entire universe because photons continue moving unless they are absorbed or scattered. The real limitation isn't distance itself, but how much light survives the journey and whether the telescope can detect it above background noise.
There are, however, two main effects that limit what we can see in visible wavelengths.
- Inverse-square dimming:
Light spreads out as it travels. The brightness we receive decreases as 1/r2. A star twice as far away appears four times dimmer. Eventually the light becomes fainter than the sensitivity of the telescope and detector. Modern large telescopes can detect galaxies billion of light-years away because they collect enough photons over long exposures.
- Absorption and scattering by gas and dust
Interstellar and intergalactic dust strongly absorbs and scatters visible light (this is called extinction). A dense molecular cloud can block nearly all visible light, which is why stars behind it are invisible in optical images but detectable in infrared or radio. So even a nearby star can be hidden, while a very distant galaxy may still be visible if the path is clear.
There is also a cosmological limit. Very distant objects are redshifted by the expansion of the universe. Their emitted visible light is stretched into infrared by the time it reaches Earth. This is why extremely distant galaxies (early universe) can't be observed well in visible light.
