Inspect the fluorescent tube to see if the dimmed area is at the center, not the ends. If this is the case, the fluorescent tube is new and must be burned-in to fully illuminate. Leave the light on for a minimum of 30 hours so that the mercury content inside the tube can fully illuminate the entire length before turning it off.
Check the temperature around the fluorescent light fixture with a handheld thermometer. Turn the heat on in the house if the temperature is 50 degrees Fahrenheit or lower as this causes the gas in the fluorescent tube to react sluggishly to the electric current. Turn the heat off once the ambient temperature around the fluorescent light fixture is well above 50 degrees.
Turn off the fluorescent light and let it cool down for a half hour. Twist and remove the fluorescent tube out of the fixture slots with a counterclockwise turn. Realign the pins at each end of the tube with the slots and slide the tube back into place. Twist the tube clockwise to properly lock the pins in position. Aim a flashlight at the end cap of the tube to verify that the ridge on the cap is aligned with a marking on the slot.