Airplay on MacBook Air

I DON'T HAVE AN APPLE TV

WHAT I HAVE ARE

1. MacBook Air (13-inch, Mid 2012)

2. iPhone 5

Model = MD297HN/A

Version = 6.1.4 (10B350)

I have a broadband connection with a wifi Modem to which I connect both my devices.

I want to see the iPhone mobile screen on the Mac

What I do:

1. I log on to the wifi router from my iPhone

2. I logn on to the wifi router from MacBookAir

WHAT HAPPENS

@ iPhone: AT TIMES THE IPHONE SHOWS THE "Airplay" icon when the home button is pressed. (THIS IS ANYWAY ARBITRARY. I TRIED DIFFERENT COMBINATIONS AND COULD NOT DEDUCE WHEN IT SHOWS AND WHEN NOT "EVEN WHEN IT IS SEAMLESSLY CONNECTED TO THE ROUTER AND LIVE ON INTERNET"

@ MacBookAir: Does not show the "Airplay" icon in the menu bar NOR in itunes.

MY QUESTION:

EVEN AS I AM HAVING AN iPhone AND A MacBook Air WHICH ACCORDING TO APPLE WEBSITE CAN COMMUNICATE THROUGH "AirPlay" WHY AM I NOT ABLE TO DO IT?

NOTE: THIS IS WHAT "APPLE SUPPORT " WEBSITE TOLD ME

Requirements for AirPlay Mirroring in OS X Mountain Lion

An Apple TV

Apple TV (2nd or 3rd generation) with software update v5.0 or later. See How to update Apple TV software.

Supported MacsAirPlay Mirroring in OS X Mountain Lion takes advantage of the hardware video encoding capabilities of 2nd and 3rd Generation Intel Core processors. Hardware video encoding allows AirPlay Mirroring to efficiently deliver high frame rates while maintaining optimal system performance. The following Mac models have processors that support AirPlay Mirroring:

• iMac (Mid 2011 or newer)
• Mac mini (Mid 2011 or newer)
• MacBook Air (Mid 2011 or newer)
• MacBook Pro (Early 2011 or newer)

Which Mac do I have?

A network

AirPlay Mirroring requires either a Wi-Fi (802.11 a/g/n) connection or an Ethernet connection to the same local network that your Apple TV uses.

HUMBLE REQUEST With the information given above, experts are humbly requested not to ask me

1. What is your Apple TV Model (I don't have one)

2. Are you connected to the same router on both the device (expalined above)

3. Have you checked whether the devices are compatible (Apple support tells me they are, as above)

4. You have to slide past the music play buttons beyond the "portrait lock screen icon" to see the Airplay button (All that and more have already been done.)

5. Look at the iTune screen on your MacBook Air to see the Airplay (I have already clarified these above)

The problem is very serious. If I am not able to MIRROR MY IPHONE SCREEN ON TO MY MACBOOKAIR in spite of having devices as per Apple specifications, and performing as per Apple instructions, then Apple is cheating me.