The correct answer is option 'C', which states that the sun is directly overhead at noon on 21st June at 23.5°N. To understand why this is the correct answer, let's break down the concept of the sun's position at different latitudes on the summer solstice.

The Summer Solstice:
- The summer solstice occurs on 21st June in the Northern Hemisphere.
- It is the day with the longest period of daylight and marks the official start of summer.
- On this day, the sun reaches its highest point in the sky, resulting in the longest period of daylight.

The Tropic of Cancer:
- The Tropic of Cancer is located at approximately 23.5°N latitude.
- It is the northernmost point where the sun is directly overhead at noon on the summer solstice.
- This latitude marks the boundary where the sun's rays are perpendicular to the Earth's surface at noon on this specific day.

Explanation:
- Option 'A', the equator, is incorrect because on the summer solstice, the sun is not directly overhead at this latitude. The equator experiences the sun directly overhead twice a year during the equinoxes.
- Option 'B', 23.5°S, is also incorrect because this latitude is located in the Southern Hemisphere, and the summer solstice primarily affects the Northern Hemisphere.
- Option 'C', 23.5°N, is the correct answer because it represents the Tropic of Cancer, which marks the northernmost point where the sun is directly overhead at noon on the summer solstice.
- Option 'D', 66.5°N, is incorrect because it is well within the Arctic Circle, and on the summer solstice, the sun can be seen above the horizon for 24 hours but not directly overhead.

In conclusion, the sun is directly overhead at noon on 21st June at 23.5°N, which corresponds to the Tropic of Cancer. This latitude marks the northernmost point where the sun's rays are perpendicular to the Earth's surface on the summer solstice.