In the morning, twilight is when the sun hasn’t yet risen but the sky is already illuminated by the sun from below the horizon. In the evening, the same thing happens after the sun has dipped below the horizon, but sunlight is still making its way over the horizon to illuminate the sky. The atmosphere scatters the sunlight so some of it gets reflected back down to the ground, illuminating the surroundings and brightening the sky.
The lower the sun dips, the less of its light makes it over the horizon. When it reaches 18° below the horizon, the brightness becomes nearly 0 and that’s when true night begins (or ends). The period after sunset but before this point is called “dusk”, and the period after the sun comes back above -18° but before sunrise is called “dawn”.
Twilight can be subdivided into three phases: civil, nautical and astronomical twilight, and they end at -6°, -12° and -18°, respectively. Civil twilight is called this way because it roughly corresponds to the period that you don’t need artificial light in towns and cities – it’s still bright enough to walk around without bumping into things. Nautical twilight gets its name from the fact that it is still bright enough for sailors to see the horizon and navigate by it. Astronomical twilight is when (though it’s not quite night yet/anymore) you can make astronomical observations of things like (reasonably bright) stars (but not fainter objects like galaxies or nebulae). Of course, these definitions are a bit overly neat (it would be a great coincidence if these experiences coincided exactly with 6-degree changes in the elevation of the sun).
How long twilight lasts depends on the season and your latitude. In some places at higher latitudes, the sun never dips below 18° at night in (mid) summer. So even though the sun does set, it never gets darker than twilight, meaning twilight (technically) lasts the whole period between sunset and sunrise. E.g. England, the Netherlands, Belgium, Poland and most of Germany never get darker than astronomical twilight in mid summer. In Scotland, Denmark and southern Sweden, it gets no darker than nautical twilight, and in Finland and Iceland it gets no darker than civil twilight. Within the polar circle, the sun doesn’t set at all in mid summer. At these higher latitudes, each phase of twilight also lasts longer.
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