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Settings - Apps and swipe to All then locate and open Camera and tap on Force stop then Clear data and Clear cache then reboot and test
You could also try performing a system repair using PC Companion as this will often fix issues - This will factory reset your phone and erase all data so best to backup before you begin
Switch off your phone and unplug from Pc (Hold volume up and power for around 10 seconds)
Start PC Companion and select Support zone then Update my phone/tablet then in Blue Repair my phone/tablet and follow the on screen instructions - When prompted connect your phone still switched off holding volume down or back button - This should start the repair or reformat process
If you are using Windows 8/8.1 or a 64bit operating system then adjust the settings for PC Companion and run in compatibility mode and chose Windows 7 or XP
If all the above fail then you would need to either return your device to the place of purchase or contact Xperia care and have your device inspected http://www.sonymobile.com/global-en/support/contact-us/
It could also be related to google now option being enabled.