A PA28 CFI WITH A STUDENT ENCOUNTER ICE ENRTE RESULTING IN ARTCC DECLARING AN EMER AND THE ACFT LNDG WITH 1 INCH OF ICE ON THE WING.

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AFTER A THOROUGH PREFLT; MY INST STUDENT AND I DECIDED WE COULD COMPLETE THE IFR TRAINING XCOUNTRY FROM BOUNTIFUL SKYPARK; UT; TO POCATELLO; ID; WITHOUT FLYING THROUGH CLOUDS OR PRECIPITATION. EVEN THOUGH WE WERE ON AN IFR FLT PLAN; WE COULD NOT OPERATE IN IMC CONDITIONS BECAUSE THERE WAS AN AIRMET OUT FOR LIGHT RIME ICE. OUR PLAN WAS DEPART SKYPARK (BTF) UNDER VFR AND CLB ABOVE THE 10000 FT LAYER WHICH STARTED ABOUT 40 NM FROM SKYPARK. OUR PLAN; IF WE COULD NOT DSND INTO POCATELLO VMC; WAS TO TURN AROUND AND START FLYING BACK FOR AN APCH INTO OGDEN; UT. WELL; IN ACTUALITY; ON OUR INITIAL CLB IT WAS VERY HAZY/SMOGGY AND DIFFICULT TO DISTINGUISH BTWN THE CLOUD LAYER AND HAZE. WE WERE ALSO VERY ATTENTIVE TO ANY ICE THAT MIGHT ACCUMULATE ON OUR WINGS. CONDITIONS WERE STILL LOOKING GOOD AND WE REQUESTED A BLOCK ALT FROM 10000-12000 FT IN ORDER TO HAVE SOME FLEXIBILITY IN OUR ATTEMPT TO CLB ABOVE OUR ANTICIPATED CLOUD LAYER. IN OUR CLB TO 12000 FT WE EVENTUALLY STARTED ACCUMULATING ICE IN THE CLOUD LAYER WE DESPERATELY TRIED TO AVOID. AT ABOUT 11500 FT; OUR CLB PERFORMANCE RAN OUT AS WE WERE SKIMMING THE TOPS OF THE CLOUDS. THE ICE CONTINUED AS WE DSNDED BACK TO 10000 FT IN SEARCH OF ICE FREE AIR. THE SEARCH WAS UNSUCCESSFUL; ABOUT 30 MI FROM POCATELLO. WE WERE UNABLE TO MAINTAIN ALT AND ZLC DECLARED AN EMER FOR US. LUCKILY WE WERE ABLE TO 'LIMP' THE AIRPLANE IN TO POCATELLO WITH ABOUT 1 INCH OF RIME ICE ALL OVER THE LEADING EDGE SURFACES. IN CONCLUSION; WE SHOULD HAVE TURNED BACK UPON REACHING THE MARGINAL HAZY CONDITIONS WHEN IT WAS UNCLR WHERE IMC STARTED. I WOULD ALSO LIKE THE FAR/AIM TO BE MORE CLR ON THE DEFINITION OF KNOWN ICING.