screen size for iPhone

I am confused. help me out here.
According to wikipedia, iPhone5’s screen resolution is 1136×640 pixels.
So i created a 2D project (new in unity 4.3), add a background image and ran it on my iPhone 5s.
Instead of showing full screen, it is showing my background small and a lot of unity default blue background around it.
How do i set up my game so that the game shows full screen?
I think i need to play with camera size, but i don’t quite have formula where i can plug in 1136 and get the right size out.
thanks

What I would do is make the texture bigger so that it could go onto the iPad.I heard this somewhere on you tube because I was wandering the same thing but for PC. But the video talked about iPods too.

Hope this helps

You have to create a script for your camera that adjust itself as per aspect ratio change.
Following code may give you some guidance what next you have to work.

// Use this for initialization
	void Start () {
		float pixelToUnit = 1/100.0f;
		float designHeight = 1536f;
		Camera.main.orthographicSize = designHeight / 2 * pixelToUnit;
	}
}