How to output my iPhone screen onto my laptop?

So I've heard you can get a HDMI output cable from apple which isn't cheap at £40 approx which can connect to any HDMI enabled input such as my TV or Laptop. I was wondering whether I should get this or use any other way (preferably free) to display my iPhone display on a bigger screen. I want it to use my entire laptop screen.
The reason I want to do this is because I want to watch films from an app I have on my phone but on a bigger screen (HD) and also using the full potential of the outputted screen. How can I do this and what is the best way?

Only way it can be done for free is if you have a Mac that is updated to Yosemite, if you have Windows or Linux then you will have to buy the Lightning>HDMI converter from Apple. This will only work IF your laptop has HDMI in, most computers have HDMI out but not in so double check before purchasing.

If it is HDMI out then you will need Lightning>VGA cable.