Sometimes bulbs "unscrew" themselves or become rotated enough for the electricity not to flow correctly over the end pins.
Do not let go of the tube while working with it in the fixture, especially when rotating it. Tubes can fall out of a fixture if not properly installed.
Fluorescent tubes are filled with mercury gas and can shatter into very small pieces. If that happens, the Environment Protection Agency recommends airing out the location of the breakage, then picking up the pieces with a damp paper cloth. The pieces must be sealed in a plastic bag then thrown away.
It's generally easy to tell when an incandescent bulb has burned out. Simply look at the filament to see if it is broken, or give the bulb a gentle shake to listen for the familiar "tinkle tinkle" of the broken filament in the bulb. Identifying the viability of a fluorescent bulb is somewhat more complicated.
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Check the ends of the tube. If they appear darkened this indicates the bulb is burned out.
Rotate the tube in the fixture if the bulb is not darkened on either end.
Remove the bulb from the fixture if the bulb is still not illuminating. Remove one of the working tubes from another fixture and replace it with the suspect tube. If it illuminates, the suspect ballast, starter, or fixture may need to be replaced. If it does not illuminate, the bulb is burned out.
Gabrielle Black has been a professional writer, artist and designer since 2002. Her theatrical designs, puppet design and construction have been featured in "Theatre Design & Technology" magazine and she has written numerous articles for various websites. She holds a Bachelor of Arts from Luther College and a Master of Fine Arts from the University of Idaho, both in stage design and painting.