A code may be necessary to mirror. This code will appear on the iPad itself.
The major benefit of this set up, aside from the obvious, is that the teacher is now completely free to roam the classroom. Please remember that it is NEVER NECESSARY to project the ibook on screen - the students have their own in front of them. Having an iPad mirrored to the TV allows the teacher to use the TV as a whiteboard - to address and clarify things that come up in class as he/she monitors.
A note about widgets: the main purpose of widgets is self-study. Mostly, these are meant as a way for students to test themselves at home. When widgets are done in class, they are not to be on screen, and the teacher is not to 'lead' the task - it should instead be treated as a group activity. The idea is to de-centralise the classroom. Use every opportunity to do so.