DURING A PLT TRAINING FLT; PLTS OF A CESSNA 172; PENETRATED THE LAX CLASS B AIRSPACE.

Narrative

I WAS FLYING WITH A STUDENT AROUND AND BELOW THE LAX CLASS B AIRSPACE; INSTRUCTING HER ON AIRSPACE AWARENESS AND AVOIDANCE. VISIBILITY AT THE TIME OF THE FLT WAS REDUCED SUBSTANTIALLY DUE TO SMOKE AND HAZE. WE WERE CIRCLING LA CITY HALL AND WHEN THE STUDENT STOPPED CIRCLING; SHE PROCEEDED TO HEAD SWBOUND ALONG THE HARBOR (110) FREEWAY MISTAKING IT FOR THE SANTA MONICA (10) FREEWAY. AT THE TIME; DUE TO REDUCED VISIBILITIES; I WAS INSTRUCTING THE STUDENT ON HOW TO USE VOR RADIALS FOR NAV AND ORIENTATION AND AT THAT TIME RECOGNIZED THE ERROR AND TOLD THE STUDENT TO TURN AROUND AND HEAD DIRECTLY TOWARDS THE LA COLISEUM. WE THEN PROCEEDED DIRECTLY TO SANTA MONICA ARPT VIA DIRECT SMO VOR AND WHEN WE CONTACTED SMO TWR; SOCAL TRACON WAS TRACKING US; AND AT THAT TIME WE WERE NOTIFIED TO CONTACT THE AREA MGR UPON LNDG; WHICH I DID AND TOOK FULL RESPONSIBILITY FOR OUR ACTIONS. HAVING FLOWN LOW LEVEL AROUND THIS AREA ON A FEW OCCASIONS; I AM QUITE CONFIDENT THAT WE WOULD HAVE NEVER PENETRATED THE CLASS B AIRSPACE IF THE VISIBILITY WASN'T SO BAD. THE TEMPORARY DISORIENTATION BY THE STUDENT (WHO IS A PVT PLT) WAS INDUCED FROM NOT BEING ABLE TO SEE THE OCEAN OR SURROUNDING FOOTHILLS. I AS AN INSTRUCTOR WAS AT FAULT FOR ALLOWING MY STUDENT TO NAV VIA PILOTAGE AS I WAS SHOWING HER RADIO NAV. I WAS ALSO IN ERROR TO CONDUCT THIS LESSON ON A DAY THAT WAS OBVIOUSLY MVFR; WHICH WAS NOT APPARENT UNTIL WE WERE IN THE DOWNTOWN AREA.