What is the time of year when the sun's most direct rays reach farthest north or south?

Similarly, around December 21, the sun is farthest south of the equator.

Around December 21

The sun's most direct rays reach farthest north or south of the equator, around December 21. This is the period of the winter solstice in the Northern Hemisphere, where the Earth is tilted away from the sun. At this time it's summer solstice in the Southern Hemisphere.