Does the Chromecast support AirPlay mirroring? I think that would be the only way it could work. You may have to use AppleTV instead.
I don't believe it is supported.
It is definitely NOT supported. Although you can now mirror more recent android based phones on chromecast with a revision that was released in July, it still does not support iOS devices on mirror.
AppleTV supports mirroring from iOS, including the older 2nd Gen AppleTV's which are a bit cheaper used.