Effect of WiFi on a laptops battery life
Wireless radio (Wi-Fi) requires power (which is measured in decibel milliwatts dBm). The Wi-Fi will utilize battery power whenever the radio is switched on. Older adapters will use power regardless of work being done as radio is kept on throughout. However the newer ones have the WMM power save intelligence function which conserves power up to 40% more than other systems.
The Wi-Fi power save poll protocol created by less watts.org for the Linux system saves power by powering off the adapter for short periods to save power.
Research is being conducted on the idea of solar powered adapters/routers. But to clarify the actual concern here the battery life is affected by factors such as the quality and type of battery, the wireless radios Dbm rating, how long it is kept on, whether or not there are any power saving modes being used and the power requirements of the computers other components (separate from the wireless radio). You can check out the differences caused by using Wi-Fi by comparing it with a battery that has not been used for supporting wireless networking.