The Joule Thief is by now a well-known type of circuit for driving an LED from a single cell battery. The circuit boosts the battery voltage to the 3.5 volts or so that a white LED needs, and continues working until the battery has been drained down to around 0.5V. This is the voltage at which the single transistor in the circuit can no longer function, so everything stops. At this point you can feel pretty good knowing that you've made use of virtually all the energy that battery had to give. The light will get a little less bright as the battery wears down, but it is still an effective night light near the very end. You can even make use of batteries that have become too weak to brightly light your flashlight or play your radio. One of the author's radios refuses to play when it has run the batteries down to around 1.2 Volts, but there is still enough energy in them to keep one of these electronic night lights going for a month or two!