Yes, I have done the same as mark and Kerry, and it works fine.
But if I remember rightly, it was a pretty expensive adapter (Like everything Apple!) so it may be cheaper to go with chromecast??
Just read up on the use of Chromecast before you buy.
I believe the phone and the Chromecast device need to be on the same WIFI network first so the phone can "cast" the image to the device via the WIFI.
Hence another device (a WIFI router) may be needed.
The Chromecast generally works well but it does use more data and you will need to be on WiFi.
We dont use our Chromecast anymore as we bought an HDMI adapter and connect with that. The adapter was $69 from memory from JB HiFi but they are available on eBay. I cant say wether the EBay ones are the same.
Our adapter provides a plug to charge the phone as you are mirroring to TV.
It also means that you dont have to have wifi and can use very cheap data like what we subscribe to from BOOST, for our phone service.
We havent used our Chromecast for about two years since realising the data use was cheaper with the HDMI adapter.