Answer:
Point Barrow, Alaska is at a latitude of 71.3 degrees north. For five weeks around the winter solstice, the Sun never gets to the horizon, and you experience continuous darkness.
On November 19, the Sun rises almost due south at Point Barrow, at 1:06 PM. The Sun barely rises above the horizon, and sets 12 minutes later. For the next week or so, the simultaneous glow of sunrise/sunset appears along the southern horizon, and it stays twilight with the Sun just below the horizon, and then it gets dark again. By the end of November, there is no twilight left at all. And the Sun stays down for nearly 2 months.
By the middle of January, a hint of twilight begins to peek up in the middle of the day, and the Sun finally rises on January 23, at 1:05 PM. But don't get used to it; the Sun sets again an hour later.
The flip side of this, of course, is that the Sun never SETS from the middle of May until the beginning of August. Which is why people call Alaska the "Land of the Midnight Sun". It's not just a tourist slogan!