If the three-way bulb on one of your table or floor lamps has only one level of light, more than likely one of the filaments has burned out. However, it could also be a connection in the three-way socket. Follow these steps to try and figure out the problem.
Caution: It is very important to unplug the lamp from the wall outlet, or extension cord, before proceeding with a repair of the electrical socket.
Take a small, pointed knife and slightly lift up the loose end of the springy metal tongue right in the middle of the socket. Then make a few scrapes on that tongue for a cleaner contact point. Do the same for the small rigid peg close to one edge of the socket. Screw in the bulb and plug in the lamp.
If it still does not work, then one of the filaments has burned out.
A three-way bulb has two filaments. The switch turns on either one or the other, or both filaments. For example, a 50-100-150, three-way light bulb has two filaments. One is 50 watts and the other is 100 watts. When both are on, the light output is the full 150 watts.
While you’re working on the socket, check the electrical cord. If you have previously used electrical tape to fix ripped insulation damaged by your vacuum cleaner, the cord should be replaced.
Sometimes this is not easy. Over the years, the standard 18-2 gauge lampcord has required thicker insulation. It may be harder to feed the bigger cord through the threaded pipe. If you cannot do it, have a professional do the repair. It could prevent a future fire.