The use of t he ellipsometer for t he m eas urpment of the thickn ess a nd refra ctive index of very thin film s is reviewed . The P o in care sphere representatio n of t he state of p ola rizat io n of light is de \'elop ed a nd used to desc ribe t he reflection process. D etails of the operation of t he ellipso meter a rc examined criticall y. A co mpu tatio nal mC'thod is prese nted by whi ch the thickness of a film of known refractive ind ex on a re fl ecting s ubstrate of known optical co nstants ma y be calculated direc t ly from the ellipsometer r ea din g~. A met hod for co mpu tin g both the refractivc index a nd thickn ess of an unkn own film is also d e veloped. These meth ods have been applied to the det erminat ion of th e th ick ness of a n adso rbed water layer on chromium ferrotyp e p la t es and on gold s urfaces. In th c former case the t hi ck ness , ras 23 to 27 A, a nd in the lat,tc r was 3 to 5 A. Th e meas urement of the th ickness and refractive index of barium fiu ori de film s c\'aporated 0 11 ch romiu m fC'ITotyp e s urfaces is used a s a n illust ration of t h e simu ltaneous d eterlllin a tion of these t wo qu a ntiti es .

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