How can compact fluorescent bulbs use only 13 Watts and put out the equivalent of 60 Watts?

The first thing to understand is the construction of each type of bulb. The light from an incandescent bulb is generated by sending a lot of electricity through a tungsten filament which causes it to get white hot. A compact fluorescent (CFL) lamp however, is filled mostly with mercury gas. As electricity pulses through the mercury vapor, the energy associated with the electrons on the mercury atoms increases. Because the electricity is pulsed on and off, electrons eventually lose the extra energy, and they release the extra energy in the form of emitted light.

The key difference here is in the colors that are emitted, and to illustrate the difference I have analyzed each type of bulb with an optical spectrometer, a device which analyzes light signals and determines what "color", or wavelengths" are present. Both bulbs were analyzed within minutes of each other. Both bulbs were allowed the same amount of time (minutes) to warm up, and were analyzed at the same distance and spectrometer settings. Here is the plot showing the two types of bulbs:

The point of this graph is to show that the incandescent bulb emits light not only in the visible spectrum, but also in the infrared region that we can't see. That means that 42% of the tungsten bulbs efforts are wasted, and we haven't even talked about energy losses to the heat generated in this kind of light bulb. Considering the CFL bulb, humans can see 95% of the light that is emitted, and these bulbs generate less heat.

So, in basic terms, a tungsten bulb is wasting a lot of energy. But, tungsten bulbs still have a healthy self-esteem because they will never be as toxic to the environment as the mercury in the CFL's.