Question
I am propagating begonias indoors and would like to know when and for how long should they be exposed to artificial light, if required, of course.

Answer
To flower, Begonias need Far Red (from incandescents) to supplement Far Blue (from fluorescents) light.  Please tell me a little more about which Begonias you are growing, and how you are propagating them.  I am assuming also that you are not going to have access to a window or skylight?  rsvp