Option 1: 49° - This latitude does not experience sunlight for 24 hours on the longest day.

Option 2: 66 1/2° - This latitude, also known as the Arctic Circle, is correct. On the longest day of the year (summer solstice), areas north of the Arctic Circle experience continuous daylight for 24 hours.

Option 3: 63° - This latitude does not receive 24 hours of sunlight on the longest day.

Option 4: 69°51` - This latitude, close to the Arctic Circle, also experiences 24 hours of sunlight on the longest day. However, option 2 is the better answer as it provides a rounded latitude value commonly associated with the Arctic Circle.

Therefore, the correct answer is option 2, 66 1/2°.