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# INTERMEDIATE LAB A PHY 3802L

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This 15 page Class Notes was uploaded by Garett Kovacek on Thursday September 17, 2015. The Class Notes belongs to PHY 3802L at Florida State University taught by Staff in Fall. Since its upload, it has received 7 views. For similar materials see /class/205539/phy-3802l-florida-state-university in Physics 2 at Florida State University.

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Date Created: 09/17/15

104 Re ection of polarized light from dielectrics 1 Purpose 2 Apparatus Fresnel39s equations Verify Fresnel s Equations of Re ection Gaertner Scienti c spectrometer two polarizers monochromatic light source 3 Procedure The re ectance of a dielectric for light at nonnormal incidence is dependent on the polarization of the incident light a b V Align the spectrometer With unpolarized quotmonochromaticquot light falling on the face of the prism and the angle between the telescope and collimator around 115 place a piece of polaroid in the telescope beam By making adjustments in the orientation of the polaroid and the incident angle obtain a minimum in the re ected intensity The minimum corresponds to a plane polarization of the incident light such that the electric vector is parallel to the surface The angle of incidence for complete polarization is called Brewster s angle and it is given by n tan i Obtain a value for n and compare with the value obtained by other means Place a polaroid in the incident beam oriented at 450 so as to put equal components of both polarizations into the prism Using a range of values for i rotate the analyzer polaroid for maximum extinction Determine the angle of the analyzer relative to the plane of incidence for the above measurements and obtain the ratio of the amplitudes of the two components of the re ected light Plot and compare your results with the theoretical curve See explanation below 103 Measurement of the dispersion of glass with a prism spectrometer 1 Purpose Measure Dispersion Relation of a Glass Prism in the Visible Spectrum 2 Apparatus Gaertner Scienti c Spectrometer Hg and He lamps 3 Introduction The deviation produced by a prism depends on the angle of incidence i the refracting angle of the prism 0c and the index of refraction n For a given setting of a prism in a spectrometer a dispersed spectrum is observed showing a variation of the angle of deviation with wavelength This is due to a dependence of the refractive index n on the wavelength 7 We may express the dependence by putting dSdk dSdn dn d7t l The rst factor dSdn depends on the conditions of the experiment but the second dnd is a function only of the material of the prism and is called dispersion of the material This is the quantity that we wish to study The index of refraction for any wavelength can be determined from the relationship n sin a62 sina 2 where at is the refracting angle of the prism and 5 is the angle of minimum deviation for the particular wavelength used The value of n can thus be obtained experimentally for any 7 at which we have a spectral line available and an experimental curve of 71 versus 7 can be made Although it is in general difficult or impossible to derive theoretically a satisfactory formulation of the dependence of n on 7 the experimentally determined curve can be tted with a fair degree of accuracy except in the neighborhood of strong absorption bands of the material by an empirical equation due to Cauchy This equation is 2 n A 303 3 where A and B are constants for a given substance The dispersion of the material is obtained from equation 3 by differentiating with respect to the wavelength dn m mm3 4 The problem of the experiment is therefore essentially that of determining the constants in Cauchy39s equation 3 Procedure 31 Apparatus The spectrometer will probably not be in adjustment so this must be done first The adjustment for parallel light should be made by the Gauss eyepiece method In order to measure the refracting angle of the prism place it on the spectrometer table so that the angle at is toward the collimator and so that light from the collimator strikes both refracting faces An image ofthe slit re ected in each face can be seen in the telescope by moving the telescope but not the prism Measure the angle between the two images of the slit Show in the writeup that it is equal to 20 note that the refracting angle at of the prism is called A in the gure below EEO 2A The positions of minimum deviation for each line used should be determined with the prism set to refract in the light first to one side of the straight through beam and then to the other The difference between these two positions will give 25 The position of minimum deviation for the spectral line is found by rotating the prism until the position is found where the line moves away from the direction of the incident light regardless of which way the prism is turned The position of the prism for minimum deviation is of course different for each different wavelength and therefore must be redetermined for each line The following table gives the spectral lines from the helium and mercury sources which are to be used in this experiment 32 Spectrum lines to be used 2 3 4 6 7 10 Source 7 nm 17 2 nm39z 17 4 nm394 Description He 7065188 2003303x10396 40133322x103912 Farthestred Hg 623437 25728523 66195689 Weak but strongest in its region He 5875618 28966291 83904602 Bright yellow Hg 5460753 33534739 112457874 Bright green He 5016675 39750374 158009226 Bright greenmiddle one of3 fairly close lines He 4713143 45017230 202655096 Blue He 4471477 50014738 250147400 Bright blueviolet Hg 4358338 52645128 277150948 Bright blueviolet Hg 4046571 61069683 372950621 Bright violet brighter and shorter of two fairly close lines He 3888646 66130709 437327069 Farthest violet 33 Calculations 1 2 3 4 Tabulate 7t 5 and 7 calculated from equation 2 for all lines Plot a graph with index of refraction as ordinate and wavelength as abscissa Assuming that Cauchy s equation gives the correct form of the relationship between 71 and 7t calculate the least square straight line for 71 vs 17t2 that is an equation of the form n A B17t2 Plot this line on a graph with n as ordinate and 17 2 as abscissa Show the experimental points on the same graph Write on the graph your values of A and B Using equation 3 and your values ofA and B calculate n for 7 200 500 800 nm giving the standard deviation for each Using equation 4 and your value of B calculate dnd7t for 7 200 500 800 nm giving the standard deviation for each 34 Notes on the application of the least square method m The abscissae 103 may be taken as exact therefore the transformation of coordinates from 7 to 17 2 in order to make the curve a straight line does not change the weighting Although the individual measurements of angles for different wavelengths may reasonably be assumed to have the same weights the n 5 calculated from them will not In fact you can verify that if it is assumed that 6a 65 6 then 1 g m 62 n cos20c5262 4m wm m wm However for ac 60 and 5 50 6201 1047 62 and for ac 60 5 55 6201 1143 62 Thus in the range in which the measurements are made 620 and hence the weighting of n varies by only about 9 percent We are therefore justified in making the simplifying assumption that the n s are equally weighted if the 5 s are and the 5 s will be if the number of measurements of each is the same The appearance of the quotfitquot of the least squares curve to the experimental points should be observed critically both as a check on the calculations leading to the line and to notice if the residual show any trends which might suggest an improvement of the original assumptions In fact Cauchy s equation is known to give a better fit if it is given as nAEVOMW and this may very likely show up in your results IM1 FranckHertz Experiment 1 Purpose Perform the historic FranckHertz experiment to demonstrate the existence of discrete energy levels in mercury and to determine the minimum kinetic energy needed by an electron in order to collide inelastically with a mercury atom 2 Apparatus Keithley 600 A Electometer Power Supply 0 to 40 V DC for accelerating voltage Power supply or transformer 63 V AC for heating of cathode FranckHertz tube with heating oven 15 V battery 2 Voltmeters X Y plotter 63VAC POWER 030VDC 39139 SUPPLIES Fl y y u i u X 105 Output X Electrometer Note 100KQ 39 1 5 V Resistor is in circuit A I 39 r r in order to protect tube 100 Kg 39 ICoaxial inside tube housing quot Connector fk lt E1 2m Collector f Electrode X Y Recorder 0 V o gt gt xfg r 3 Description of experiment The FranckHertz tube serves primarily as an enclosed atmosphere of mercury vapor through which electrons are accelerated by means of a variable potential difference so that a range of electron energies is available The tube has three electrodes an indirectly heated cathode as an electron source a grid form anode to which the accelerating potential difference is applied and a plate which serves as an electron collector A sensitive electroscope is connected to the collector electrode so that the number of electrons reaching the collector plate may be measured The mercury atmosphere is kept at the desired pressure by heating the tube in an electric oven the temperature of the oven being controlled by thermostat Between the anode and the collector plate a small constant negative potential of 15 volt is applied This is called the retarding voltage and makes it necessary for an electron at the grid anode to have at least 15 eV energy in order to reach the collector plate As shall be shown later this retarding voltage helps to differentiate the electrons having inelastic collisions from those not having collisions As we increase the accelerating voltage we should expect the following to happen Up to a certain voltage say V1 the plate current will increase as more electrons reach the plate When we reach V1 we note that the plate current Ip takes a sudden drop This is due to the fact that the electrons just in front of the gridanode have gained enough energy to collide inelastically with the mercury atoms Having given all their energy to the mercury atom they do not have sufficient energy to overcome the retarding voltage between gridanode and collector electrode This causes a decrease in the plate current 1p Now as the voltage is again increased the electrons obtain the energy necessary for inelastic collisions before they reach the anode After the collision by the time they reach the grid they have obtained enough energy to overcome the retarding voltage and will reach the collector plate Thus Ip will increase Again when a certain voltage V is reached we note that Ip drops This means that the electrons have obtained enough energy to have two inelastic collisions before reaching the grid anode but have not had enough remaining energy to overcome the retarding voltage Increasing the voltage again Ip starts upward until a third value V3 of the voltage is reached when Ip drops This corresponds to the electrons having three inelastic collisions before reaching the anode and so on The interesting fact is that V3 V2 equals V2 V1 equals approximately 49 volts which shows that the mercury atom has definite excitation levels and will not accept energy except in quantized amounts namely 49 electron volts When an electron has an inelastic collision with a mercury atom it gives up all its energy to the atom This transfer of energy causes one of the outer orbital electrons to be pushed up to the next higher energy level This excited electron will within a very short time fall back into the ground state level emitting energy in the form of photons The original bombarding electron is again accelerated toward the grid anode We see then that the excitation energy can be measured in two ways by the method outlined above or by spectroscopically analyzing the radiation emitted by the excited atom The latter of these two methods is by far the more difficult to perform 4 Caveat Protect the tube from damage The pressure of the mercury in the tube is a critical factor If this pressure is too low the mean free path of the electrons is too great the probability of collision lowered thus some of the electrons would gain more energy than necessary for an inelastic collision with the mercury atom If this energy were to equal or exceed the ionization potential of mercury the mercury would ionize causing a rapid discharge at the plate into the electroscope The ionization potential of mercury is approximately 104 electron volts The manufacturers of the tube suggest a pressure of 15 to 20 mm of mercury within the tube This corresponds to a tube temperature of around 1800C Maintaining the correct temperature of the oven is a critical issue in this experiment Never operate the tube at temperatures outside the range 1500C to 2000C Contact potentials Consideration of contact potentials is also necessary In simple terms this means that the accelerating potential is not completely converted into kinetic energy of the electrons some of it provides the work function of the cathode material ie the amount of energy measured in electron volts necessary to free the electrons from the cathode The cathode is coated with a material with a relatively low work function The collector plate since it is used merely as electron collector has a somewhat higher work function The contact potential is the difference between the work functions since they are oppositely directed in the electric field that is the electric field has to work against the cathode potential but is helped in the case of the collector plate Thus we should expect that the voltage to the first peak will be greater than the average peak to peak voltage due to the contact potential The contact potential can be calculated as the average peak to peak voltage subtracted from the first peak voltage Notes 1 The data are recorded on a XY plotter The recorder has two inputs Xaxis and Yaxis both of which have high input impedances so that they affect the remaining circuit very little ie the XY recorder is equivalent to two voltmeters In this experiment the Xaxis measures the accelerating voltage on Va between cathode and gridanode and the Yaxis measures the plate current Thus a graph of plate current versus accelerating voltage is obtained directly on the XY recorder 2 When using the XY recorder the electrometer should be operated in the quotfastquot mode The mode is determined by a switch on the back of the electrometer 3 In case the XY plotter does not work you have to use a voltmeter instead and set the accelerating voltages by hand and record the output voltage proportional to the current of the electrometer 4 A 100 kg current limiting resistor is incorporated in the circuit between the connecting 103 Measurement of the dispersion of glass with a prism spectrometer 1 Purpose Measure Dispersion Relation ofa Glass Prism in the Visible Spectrum 2 Apparatus Gaertner Scienti c Spectrometer Hg and He lamps 3 Introduction The deviation produced by a prism depends on the angle of incidence i the refracting angle of the prism 0c and the index of refraction n For a given setting of a prism in a spectrometer a dispersed spectrum is observed showing a variation of the angle of deviation with wavelength This is due to a dependence of the refractive index n on the wavelength 1 We may express the dependence by putting d dk d dn dn d7 1 The rst factor d dn depends on the conditions of the experiment but the second dnd is a function only of the material of the prism and is called dispersion of the material This is the quantity that we wish to study The index of refraction for any wavelength can be determined from the relationship n sin 06 62 sina 2 where 0c is the refracting angle of the prism and 5 is the angle of minimum deviation for the 2 particular wavelength used The value of n can thus be obtained experimentally for any 7 at which we have a spectral line available and an experimental curve of 71 versus 7 can be made Although it is in general dif cult or impossible to derive theoretically a satisfactory formulation of the dependence of n on 7 the experimentally determined curve can be tted with a fair degree of accuracy except in the neighborhood of strong absorption bands of the material by an empirical equation due to Cauchy This equation is n A 112 3 where A and B are constants for a given substance The dispersion of the material is obtained from equation 3 by differentiating with respect to the wavelength dn m mm3 4 The problem of the experiment is therefore essentially that of determining the constants in Cauchy s equation 3 Procedure 31 Apparatus The spectrometer will probably not be in adjustment so this must be done first The adjustment for parallel light should be made by the Gauss eyepiece method In order to measure the refracting angle of the prism place it on the spectrometer table so that the angle 06 is toward the collimator and so that light from the collimator strikes both refracting faces An image of the slit re ected in each face can be seen in the telescope by moving the telescope but not the prism Measure the angle between the two images of the slit Show in the writeup that it is equal to 206 note that the refracting angle 06 of the prism is called A in the figure below The positions of minimum deviation for each line used should be determined with the prism set to refract in the light first to one side of the straight through beam and then to the other The difference between these two positions will give 25 The position of minimum deviation for the spectral line is found by rotating the prism until the position is found where the line moves away from the direction of the incident light regardless of which way the prism is turned The position of the prism for minimum deviation is of course different for each different wavelength and therefore must be redetermined for each line The following table gives the spectral lines from the helium and mercury sources which are to be used in this experiment 32 Spectrum lines to be used 2 3 4 6 7 10 Source 7 nm He Hg He Hg He He He Hg Hg He 1amp2 nm39z 1x4 nm394 7065188 2003303x10396 40133322x103912 623437 25728523 66195689 5875618 28966291 83904602 5460753 33534739 112457874 5016675 39750374 158009226 4713143 45017230 202655096 4471477 50014738 250147400 4358338 52645128 277150948 4046571 61069683 372950621 3888646 66130709 437327069 33 Calculations 1 2 3 4 Description Farthest red Weak but strongest in its region Bright yellow Bright green Bright greenmiddle one of 3 fairly close lines Blue Bright blueviolet Bright blueviolet Bright violet brighter and shorter of two fairly close lines Farthest violet Tabulate 7M 5 and 7 calculated from equation 2 for all lines Plot a graph with index of refraction as ordinate and wavelength as abscissa Assuming that Cauchy s equation gives the correct form of the relationship between 71 and 7M calculate the least square straight line for 71 vs 112 that is an equation of the form n A B12 Plot this line on a graph with n as ordinate and 1702 as abscissa Show the experimental points on the same graph Write on the graph your values of A and B Using equation 3 and your values ofA and B calculate n for 7 200 500 800 nm giving the standard deviation for each Using equation 4 and your value of B calculate dnd for 7 200 500 800 nm giving the standard deviation for each 103 Measurement of the dispersion of glass with a prism spectrometer 1 Purpose Measure Dispersion Relation ofa Glass Prism in the Visible Spectrum 2 Apparatus Gaertner Scienti c Spectrometer Hg and He lamps 3 Introduction The deviation produced by a prism depends on the angle of incidence i the refracting angle of the prism 0c and the index of refraction n For a given setting of a prism in a spectrometer a dispersed spectrum is observed showing a variation of the angle of deviation with wavelength This is due to a dependence of the refractive index n on the wavelength 1 We may express the dependence by putting d dk d dn dn d7 1 The rst factor d dn depends on the conditions of the experiment but the second dnd is a function only of the material of the prism and is called dispersion of the material This is the quantity that we wish to study The index of refraction for any wavelength can be determined from the relationship n sin 06 62 sina 2 where 0c is the refracting angle of the prism and 5 is the angle of minimum deviation for the 2 particular wavelength used The value of n can thus be obtained experimentally for any 7 at which we have a spectral line available and an experimental curve of 71 versus 7 can be made Although it is in general dif cult or impossible to derive theoretically a satisfactory formulation of the dependence of n on 7 the experimentally determined curve can be tted with a fair degree of accuracy except in the neighborhood of strong absorption bands of the material by an empirical equation due to Cauchy This equation is n A 112 3 where A and B are constants for a given substance The dispersion of the material is obtained from equation 3 by differentiating with respect to the wavelength dn m mm3 4 The problem of the experiment is therefore essentially that of determining the constants in Cauchy s equation 3 Procedure 31 Apparatus The spectrometer will probably not be in adjustment so this must be done first The adjustment for parallel light should be made by the Gauss eyepiece method In order to measure the refracting angle of the prism place it on the spectrometer table so that the angle 06 is toward the collimator and so that light from the collimator strikes both refracting faces An image of the slit re ected in each face can be seen in the telescope by moving the telescope but not the prism Measure the angle between the two images of the slit Show in the writeup that it is equal to 206 note that the refracting angle 06 of the prism is called A in the figure below The positions of minimum deviation for each line used should be determined with the prism set to refract in the light first to one side of the straight through beam and then to the other The difference between these two positions will give 25 The position of minimum deviation for the spectral line is found by rotating the prism until the position is found where the line moves away from the direction of the incident light regardless of which way the prism is turned The position of the prism for minimum deviation is of course different for each different wavelength and therefore must be redetermined for each line The following table gives the spectral lines from the helium and mercury sources which are to be used in this experiment 32 Spectrum lines to be used 2 3 4 6 7 10 Source 7 nm He Hg He Hg He He He Hg Hg He 1amp2 nm39z 1x4 nm394 7065188 2003303x10396 40133322x103912 623437 25728523 66195689 5875618 28966291 83904602 5460753 33534739 112457874 5016675 39750374 158009226 4713143 45017230 202655096 4471477 50014738 250147400 4358338 52645128 277150948 4046571 61069683 372950621 3888646 66130709 437327069 33 Calculations 1 2 3 4 Description Farthest red Weak but strongest in its region Bright yellow Bright green Bright greenmiddle one of 3 fairly close lines Blue Bright blueviolet Bright blueviolet Bright violet brighter and shorter of two fairly close lines Farthest violet Tabulate 7M 5 and 7 calculated from equation 2 for all lines Plot a graph with index of refraction as ordinate and wavelength as abscissa Assuming that Cauchy s equation gives the correct form of the relationship between 71 and 7M calculate the least square straight line for 71 vs 112 that is an equation of the form n A B12 Plot this line on a graph with n as ordinate and 1702 as abscissa Show the experimental points on the same graph Write on the graph your values of A and B Using equation 3 and your values ofA and B calculate n for 7 200 500 800 nm giving the standard deviation for each Using equation 4 and your value of B calculate dnd for 7 200 500 800 nm giving the standard deviation for each 34 Notes on the application of the least square method a b The abscissae lkz may be taken as exact therefore the transformation of coordinates from k to UK2 in order to make the curve a straight line does not change the weighting Although the individual measurements of angles for different wavelengths may reasonably be assumed to have the same weights the n 5 calculated from them will not In fact you can verify that if it is assumed that 5a 55 039 then 1 sin2 52 02 n cos2X52 0392 4 sin2 002 sin2 002 However for 0L 600 and 5 50quot 5271 1047 0392 and for 0L 60 5 55quot 5271 1143 0392 Thus in the range in which the measurements are made 62n and hence the weighting of n varies by only about 9 percent We are therefore justified in making the simplifying assumption that the n s are equally weighted if the 5 s are and the 5 s will be if the number of measurements of each is the same The appearance of the quotfitquot of the least squares curve to the experimental points should be observed critically both as a check on the calculations leading to the line and to notice if the residual show any trends which might suggest an improvement of the original assumptions In fact Cauchy s equation is known to give a better fit if it is given as n A Bk2 Ck4 and this may very likely show up in your results

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