macbook pro & sony projector problem

If the projector does not show under Display Preferences then no mirroring option will show since there is nothing to mirror to.

Try the following but it could be a bad mini displayport>VGA adapter. I have had a few of those go bad or not even work initially.

- Try resetting the SMC and NVRAM/PRAM

Intel-based Macs: Resetting the System Management Controller (SMC)

https://support.apple.com/en-us/HT201295

About NVRAM and PRAM

https://support.apple.com/en-us/HT204063

- Try starting in Safe Mode

OS X: What is Safe Boot, Safe Mode?

https://support.apple.com/en-us/HT201262

What output of the Mac are you using?

What input on the projector are yo using?

Does the projector show in Display Preferences?

Does the cable and projector work on another computer?

Does the Mac's output work on another display device?

This is the Mac Pro desktop forum. I requested your post be moved to the MacBook Pro laptop forum.