Download another camera app from the store and try to take a picture with that one, if the black screen still appears, you can try these options. IF all of these fail, the issue is probably related to hardware.
Soft Reset
The soft reset is the same thing as pulling your battery (on devices where that is possible). This method will not remove anything at all from your phone and is completely safe to attempt in any problem situation.
You perform the soft reset by having your phone turned on. Then press and hold the volume down + power buttons until your phone vibrates and restarts. Note that you should not touch the device screen during the process (not even when the 'slide down to power off' prompt appears).
Hard Reset
The hard reset will bring your phone back to factory settings, the same state as when the device was first turned on. All apps, messages, media, personal settings, etc will be removed from the phone. If backup is turned on under Settings, you can restore your apps and settings after performing a hard reset (as long as you initialize the phone with the same Microsoft Account). Note that resetting your device will not remove any OS or firmware updates. You will remain on the same version of Windows Phone after the reset.
If you can TURN ON your device you can reset your phone under Settings: Settings > about > reset your phone
If you can't open your device because of a forgotten PIN (or similar), you can use the button method: Press and hold the power-, volume-down- and camera buttons until the phone vibrates. Then release the power-button and keep the other two buttons pressed for another five seconds. The phone should reset to factory settings.
If both of these options failed there is one more alternative. Use the Windows Device Recovery Tool to reset your device. This will take you back to the OS version which originally came with the phone. So for phones that did not ship with W10M, the WDRT will take it back to 8.0. If the phone was shipped with W10M, the tool will take it back to a version of W10M
Follow this link for instructions and download: http://www.microsoft.com/en-us/mobile/support/faq/?action=singleTopic&topic=FA142987
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