FLC CLRED FOR VISUAL APCH TO RWY 36L LINED UP APCH TO RWY 35L. MISTAKE WAS DISCOVERED; ACFT LINED UP AND LANDED ON CORRECT RWY.

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OUR ACFT WAS CLRED FOR 'VISUAL APCH TO RWY 36L' AT DFW INTL ARPT WHEN THE FOLLOWING EVENT OCCURRED (SEE DIAGRAM ON REVERSE). WE WERE ON A L BASE FOR RWY 36L ABOUT 5 MI SW OF DFW DSNDING WHEN REGIONAL APCH CLRED US FOR A VISUAL APCH TO RWY 36L AND INSTRUCTED US TO FOLLOW COMPANY TFC ON FINAL TO RWY 36L. AT THIS POINT WE HAD TFC IN SIGHT. WE CHANGED TO TWR FREQ AND WERE CLRED TO LAND. I WAS THE PF; THE CAPT WAS PNF. AS WE CONTINUED ON BASE AND STARED THE FINAL TURN I THOUGHT IT WAS STRANGE THAT A JET WAS DEPARTING FROM OUR RWY. BOTH ME AND THE CAPT WERE SEARCHING FOR THE COMPANY TFC WHICH WE HAD NOW LOST SIGHT OF BUT WERE SURE WAS JUST AHEAD. THE DEPARTING JET SEEMED TOO CLOSE TO WHERE OUR TFC SHOULD BE. AS THE FINAL TURN WAS COMPLETED THE CAPT SAID 'THE TFC IS OVER THE VOR.' THIS ACFT TURNED OUT TO BE ANOTHER JET ON FINAL TO THE R PARALLEL; WHICH SEEMED VERY STRANGE TO ME. AT THIS MOMENT I REALIZED THE ARPT TERMINALS WERE TO OUR L AND WE WERE LINING UP ON RWY 35L! AN IMMEDIATE CORRECTION LINED US UP ON RWY 36L. THE LNDG WAS UNEVENTFUL AND NOTHING WAS SAID ON TWR OR GND FREQ ABOUT THE EVENT. THERE WAS NO CONFLICT WITH THE TFC THAT WAS LNDG ON RWY 35R. AFTER THE FLT THE CAPT AND I ATTEMPTED TO RECONSTRUCT WHAT HAD HAPPENED. IT WAS VERY STRANGE THAT WE BOTH MISSED THE ERROR. THE FOLLOWING ARE 'LINKS' IN THE CHAIN THAT SHOULD HAVE TIPPED US OFF. THE JET DEP IN FRONT OF US WAS TOO CLOSE TO HAVE ALLOWED THE COMPANY TFC TO LAND AND CLR THE RWY. ACFT NEVER LAND WITHIN 2 MI OF EACH OTHER ON PARALLEL RWYS (IE RWYS 35L AND 35R). THE VOR IS ON THE E SIDE OF THE OF THE ARPT. WE WERE BOTH SO BUSY LOOKING FOR THE TFC THAT WE DID NOT XCHK OUR NAV SYS WHICH WE BOTH SET TO THE RWY 36L LOC. I BELIEVE THERE WERE 2 IMPORTANT FACTORS THAT ALLOWED THIS SIT TO DEVELOP. THERE WAS A PARTIAL BROKEN CLOUD LAYER NEAR THE ARPT WHICH WAS CASTING A SHADOW ACROSS THE W COMPLEX (RWYS 36L/R). THERE IS A NEW PARALLEL RWY BEING BUILT ON THE E SIDE OF THE ARPT WITH A CTL TWR BTWN IT AND RWYS 35L/R. THESE 2 FACTORS I BELIEVE CONTRIBUTED TO AN ILLUSION IN THE PERIPHERAL VISION THAT WE WERE INDEED LINED UP ON THE CORRECT RWY. THE EASIEST WAY TO PREVENT THIS IS TO INSURE THAT BOTH CREW MEMBERS ARE NOT CONCENTRATING ON THE SAME TASK. I DO HOWEVER FIND IT VERY STRANGE THAT IT TOOK THE TWO OF US AS LONG AS IT DID TO DETECT THE ERROR.