AN INSTRUCTOR PLT LANDED ON THE WRONG RWY AT LNS. ERROR ADMITTED. VISIBILITY REDUCED SUN POS.

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WE WERE TRACKING THE 240 DEG RADIAL TO LRP WITH SUN AT LOW ANGLE (1/2 HR BEFORE SUNSET OR LESS). SAW ARPT AND WERE CLRED TOUCH-AND-GO ON RWY 31; ENTERING ON A R BASE. THE COMPASS WAS HARD TO READ (TO RESET DIRECTIONAL GYROSCOPE) DUE TO GLARE FROM THE SUN; BUT SAW RWY AND TURNED FINAL. IT WAS RWY 26. RIGHT AS WE CAME UP ON THE NUMBERS; I REALIZED MY MISTAKE; BUT TWR WAITED; NOT WANTING TO MESS US UP ON SHORT FINAL; TO ADVISE US THAT WE WERE CLRED TOUCH-AND-GO FOR RWY 31 AND WE HAD JUST LANDED ON RWY 26. THEY THEN SAID MAKE L CLOSE TFC FOR RWY 31; WHICH WE DID. SITUATIONAL AWARENESS WOULD HAVE ELIMINATED THIS PROB. LOOKING AT THE SECTIONAL; THE DIRECTION FROM WHICH WE'D APCH THE ARPT AND THE ARPT DIAGRAM WOULD HAVE MADE IT OBVIOUS THAT WE'D SEE AND PASS RWY 26 BEFORE REACHING RWY 31. USING THE HDG INDICATOR (SET PROPERLY) WOULD HAVE ELIMINATED THE PROB. ENRTE WE COULD HAVE TURNED AWAY FROM THE SUN TO LOOK AT COMPASS AND RESET DIRECTIONAL GYROSCOPE BEFORE ENTERING CLASS D AIRSPACE. THE STUDENT; VERY APT AND CAPABLE FOR A PRESOLO STUDENT; WAS FLYING AND I WAS INSTRUCTING ON BEFORE LNDG PROCS. FORTUNATELY THERE WAS NO CONFLICTING TFC.