Mathematisch-Naturwissenschaftliche Fakultät I Humboldt-Universität zu Berlin Institut für Physik Physikalisches Grundpraktikum.

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1 Mathematisch-Natuwissenschaftliche Fakultät I Humboldt-Univesität zu Belin Institut fü Physik Physikalisches Gundpaktikum Vesuchspotokoll Polaisation duch Reflexion (O11) duchgefüht am mit Vesuchspatne Andeas Kohe Potokoll von Sebastian Milste

2 I. Intoduction II. Squae-ooted eflectivity ove angle of incidence III. Bewste angle and index of efaction IV. Compaison to theoetical cuves V. Adjustment VI. Summay I. Intoduction The aim of this pactical was to analyse how diffeently polaised (othogonal/paallel to suface) light is eflected at a plane suface of a glass lens. In ode to gain compaable data, we measued the voltage induced by the eflected light fo diffeent eflection angles and fo othogonal and paallel polaized light sepaately. This enabled us to calculate the espective eflectivities and to plot thei squae oots ove the angle of eflection. With the help of the gaphic we wee to find the Bewste angle and compae ou esults with the theoetical cuves. At Bewste's angle none of the paallel polaized light is eflected, in othe wods, all of the paallel polaized light is efacted. Moeove, we will detemine the efactive index of the glass lens. The physical basics and the detailed objective fo this expeiment can be found in the instuction booklet (p.74-77). In this epot you will encounte a few indices with the following meanings: i - incident - eflected o - othogonal polaized p - paallel polaized m - diectly measued II. Gaphical figue of squae-ooted eflectivity ove angle of incidence Befoe taking down any values we adjusted ou voltmete so, that it showed a voltage of U 0 =0 V fo ou beam not hitting (any pat of) the detecto. In fact, afte changing the effective ange of the voltmete to the 300mV-scale duing testing the paallel polaized component, we obtained values fo U 0 diffeent fom 0, which will be consideed in the espective calculation. U 0 was continuously checked afte evey measued value. The maximum voltage U i induced by the uneflected light was taken down befoe evey seies of measuements.

3 The actual induced voltage fom ou light beam is the diffeence U =U m U 0 between the measued value U m and the voltage U 0. The systematic eo fo evey voltage measuement is u ' U =0,3 % U 2 LSD. Thus we obtain the esulting systematic eo: u U = u 2 U m u 2 U o 0,3% U m 2 2 LSD The same applies to U i : u U i =0,3 % U i 2 2 LSD Simila to the calculations of voltage, the actual angle of efaction is detemined by = m is the angle ead fom the scale fo the uneflected beam. It seves an adjusting pupose and its value is 0 =179 Evey measuement has the estimated uncetainty of u ' =0,5. This popagates to: u = 1 u ' 2 2 u' 2 = 2 2 u ' = 2 4 Eventually we calculate the squae oot of the eflectivity as follows: R= U U i ; u R = R 2 u U U R 2 u U U i i = 1 u 2 4U i U U U 4U u 2 3 U i i

4 III. Bewste angle and efactive index of the glass lens Fom the gaphic we deived the value fo Bewste's angle B. The minimum of the ed plot is appoximately at an angle of B = 56±1. Fomula (6) fom the booklet seves a elationship between the Bewste angle and the efactive indices of the two media ai and glass: tan B = n glass n ai Assuming that n ai =1,00029 and the uncetainty being negligible, we calculate the efactive index of ou lens: n glass =n ai tan B ; u n glass = n ai cos 2 B u B n glass =1,48±0,06 IV. Compaison with theoetical cuves Now, having found the efactive index, we will be able to evaluate ou figue fom II. We can substitute an expession fo g, the unknown angle of efaction, fom the law of efaction into the fomulae (4a) and (4b). This ends up in two fomulae fo the squae-ooted eflectivities: sin acsin sin Othogonal: R o = sin acsin sin tan acsin sin Paallel: R p = tan acsin sin Fo we eceived n glass =1,48±0,06 in III., we will plot the two functions R o and R p fo the mean value (blue and puple espectively) and also two fo each n glass =1,42 and n glass =1,54. (gey).the latte epesent the span of uncetainty due to the eo of n glass.

5 It is obvious that all values except those close to the Bewste angle ae below the theoetical cuves. This implies eithe that the voltage U is too low o the incident voltage U i is too high. As we detemined the incident voltage only once befoe evey seies of measuements, it is most pobable that the change of U i is an impotant influence we have not taken into consideation this fa. As we omitted to take note of the change, we can only use the theoetical values to adjust ou cuves. V. Adjustment We adjust the fomula fo R as follows: R= U U i U Solved fo U : U = U R U i U and U i ae values fom ou measuements, R is the value fo the eflectivity fo n glass =1,48. Thus we get fo evey angle the espective diffeence U. The eason why we can do so is that the theoetical eflectivity is detemined by the Bewste angle. This angle was ead off at the minimum of R p, which is independent fom the value of the incident voltage!

6 Fo the diffeence U we detemined the mean and added it to the incident voltage. To calculate the adjusted squae-ooted eflectivity R', the fomula fom II was used. U i became U i U and u U i was eplaced by U : = U R' U i U ; u = 1 R' u 2 U 4 U i U U U 4 U i U U 2 3 This was done fo R o ' and R p ' sepaately. Futhemoe, fo paallel polaized light and fo angles within the ange of the Bewste angle B = 56±1,the espective diffeences U wee not used fo the calculation of the mean. The esult is shown in the following figue: By adjusting the incident voltage, most points have moved close to the theoetical cuves. Especially fo the othogonal polaized light, we find a much bette match. Unfotunately the eo (othogonal) has inceased too, but this is due to the big diffeence befoe the adjustment: U o = 1,166V ; U p = 0,387 V ; To conclude, this adjustment shows that it might have been useful to detect the actual change duing the expeiment. At least two values, befoe and aftewads, should be taken down in ode to estimate the change. Especially fo the othogonal polaized light, the mean of the diffeence is that big, that it is vey unlikely the incident voltage being the only eason fo the deviation in IV.

7 VI. Summay The esults of this expeiment match with the expectations fom the theoetical point of view. This applies especially to the efactive index of ou glass lens. Cown glass has a efactive index of appoximately 1,5. This suppots the esult we have obtained: n glass =1,48±0,06. The visualizations of the squae-ooted eflectivities ae not as pefect. An adjustment showed that the plots do fit the theoetical cuves, but we had to sacifice too much of the accuacy. The incident voltage not being constant is not the only disegaded influence. Although the light passed though a filte, thee was not a 100% polaization of the light. The best evidence fo this, is that thee was no angle at which the light dot fom the lase completely disappeaed when analysing the paallel polaized light. All in all, this pactical is suitable fo the detemination of the efactive index and delives an useful quantified oveview of how light is eflected and polaised at an inteface of two diffeent media.