AN ECLIPSE 500 VLJ INSTRUCTOR AND STUDENT NEARLY COLLIDED WITH THE GND WHILE TAKING EVASIVE ACTION TO AVOID ANOTHER ACFT IN A CONTROLLED ARPT TFC PATTERN.

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ON A TRAINING MISSION IN AN ECLIPSE 500 VERY LIGHT JET; THE PLT-RATED (NOT TYPE RATED) STUDENT WAS THE PF. WE WERE ON FINAL TO RWY 16R. THERE WAS TFC IN THE PATTERN FOR RWY 16L. ON ABOUT A 3 MI FINAL; WE NOTICED TFC ON THE L DOWNWIND TO RWY 16L BEGINNING THE L BASE TURN. AS WE GOT CLOSER; IT BECAME CLR THAT THE TFC ON L BASE TO RWY 16L WOULD OVERSHOOT THE TURN TO FINAL TO RWY 16L. AS THE ACFT APCHED THE FINAL TO RWY 16R; I (THE FLT INSTRUCTOR) TOOK CTL OF THE ACFT AND TOOK EVASIVE ACTION TURNING R AND DSNDING TO AVOID THE OTHER ACFT. MY ATTN WAS FULLY DIVERTED TO THE CONFLICT ACFT. AFTER SEVERAL SECONDS OF FOCUS ON THE CONFLICT ACFT; I TOOK ANOTHER LOOK AT THE RWY AND REALIZED THAT I HAD DSNDED TO A VERY LOW ALT WHILE TAKING EVASIVE ACTION TO AVOID THE OTHER ACFT. I IMMEDIATELY PULLED UP ON THE FLT CTL SIDE STICK AND APPLIED FULL PWR EXECUTING A GAR. REMAINING IN THE PATTERN; I QUERIED THE TWR BY ASKING 'DID THAT GUY OVERSHOOT FINAL OR WHAT HAPPENED?' THE AIR TFC CTLR RESPONDED 'I'M NOT SURE WHAT HAPPENED.'