Physics307L:People/Osinski/Photoelectric/Matlab Code

%% Charge Time % raw data intens=[20 40 60 80 100]; tYellow20=[8.25 8.75 9.20 9.06 9.28]; tYellow40=[8.00 8.42 6.72 8.75 7.59]; tYellow60=[6.66 5.25 6.00 5.06 5.75]; tYellow80=[4.37 5.19 4.13 4.25 4.03]; tYellow100=[3.69 3.50 4.28 4.50 4.19]; tViolet20=[16.50 19.06 19.30 17.12 16.80]; tViolet40=[8.72 9.68 9.68 9.75 8.84]; tViolet60=[7.06 7.66 7.31 6.97 7.19]; tViolet80=[4.41 5.44 5.22 5.25 5.46]; tViolet100=[4.88 4.56 4.44 4.62 4.65];

% mean for each intensity MeanY20=mean(tYellow20); MeanY40=mean(tYellow40); MeanY60=mean(tYellow60); MeanY80=mean(tYellow80); MeanY100=mean(tYellow100); MeanV20=mean(tViolet20); MeanV40=mean(tViolet40); MeanV60=mean(tViolet60); MeanV80=mean(tViolet80); MeanV100=mean(tViolet100); MeanY=[MeanY20 MeanY40 MeanY60 MeanY80 MeanY100]; MeanV=[MeanV20 MeanV40 MeanV60 MeanV80 MeanV100];

% standard deviation of the mean for each intensity stdmY20=sqrt(sum((tYellow20-MeanY20).^2)/20); stdmY40=sqrt(sum((tYellow40-MeanY40).^2)/20); stdmY60=sqrt(sum((tYellow60-MeanY60).^2)/20); stdmY80=sqrt(sum((tYellow80-MeanY80).^2)/20); stdmY100=sqrt(sum((tYellow100-MeanY100).^2)/20); stdmV20=sqrt(sum((tViolet20-MeanV20).^2)/20); stdmV40=sqrt(sum((tViolet40-MeanV40).^2)/20); stdmV60=sqrt(sum((tViolet60-MeanV60).^2)/20); stdmV80=sqrt(sum((tViolet80-MeanV80).^2)/20); stdmV100=sqrt(sum((tViolet100-MeanV100).^2)/20);

% total stdm for f=20:20:100 stringy=sprintf('sum(stdmY%d + stdmV%d)',f,f) eval(stringy) end stdmfull=(0.7785+0.5803+0.4045+0.3997+0.2599)/10 stdmbetter=(0.1877+0.3529+0.2843+0.2070+0.1878+0.2273+ 0.1202+0.1927+0.0721)/9

% error bar plots figure(1) title('charge time vs. intensity for yellow and violet spectra') xlabel('intensity (percentage)') ylabel('charge time (s)') for f=20:20:100 hold on   plot(intens,MeanY,'Color','yellow') plot(intens,MeanV,'Color','magenta') Ystring=sprintf('errorbar(%d,MeanY%d,stdmY%d,*)',f,f,f) eval(Ystring) Vstring=sprintf('errorbar(%d,MeanV%d,stdmV%d,*,Color,red)',f,f,f) eval(Vstring) end legend('yellow','violet') hold off

%% Stop Voltage vs. Frequency MaxV=[2.044 1.71 1.49 .847 .716]; Color=[8.20264E14 7.40858E14 6.87858E14 5.48896E14 5.18672E14]; polV=polyfit(Color, MaxV, 1); funV=polyval(polV,Color); figure(2) hold on plot(Color,MaxV,'o'); plot(Color, funV,'color','green') title('Stop Voltage vs. Frequency') xlabel('frequency(Hz)') ylabel('stopping voltage(V)')

%% Determination of h % raw data data1 = [2.064, 1.718, 1.493, 0.849, 0.717]; data2 = [2.062, 1.731, 1.520, 0.842, 0.735]; data3 = [2.069, 1.725, 1.495, 0.850, 0.714]; data4 = [2.061, 1.725, 1.515, 0.849, 0.735]; freq = [8.20264E14, 7.40858E14, 6.87858E14, 5.48896E14, 5.18672E14];

ev = 1.602E-19; %electron charge. data1 = data1 .* ev; data2 = data2 .* ev; data3 = data3 .* ev; data4 = data4 .* ev;

% least squares fitting poly1=polyfit(freq, data1, 1) fun1=polyval(poly1,freq); poly2=polyfit(freq, data2, 1) fun2=polyval(poly2,freq); poly3=polyfit(freq, data3, 1) fun3=polyval(poly3,freq); poly4=polyfit(freq, data4, 1) fun4=polyval(poly4,freq);

% plots figure(3); subplot(2,2,1); scatter(freq, data1); hold on, plot(freq, fun1,'color','green');... title('Run1, 1st order'),xlabel('fq(Hz)'),ylabel('V'), hold off subplot(2,2,2); scatter(freq, data2); hold on, plot(freq, fun2,'color','green');... title('Run1, 2nd order'),xlabel('fq(Hz)'),ylabel('V'), hold off subplot(2,2,3); scatter(freq, data3); hold on, plot(freq, fun3,'color','green');... title('Run2, 1st order'),xlabel('fq(Hz)'),ylabel('V'), hold off subplot(2,2,4); scatter(freq, data4); hold on, plot(freq, fun4,'color','green');... title('Run2, 2nd order'),xlabel('fq(Hz)'),ylabel('V'), hold off

%calculating h h1=(fun1(end)-fun1(1))/(freq(end)-freq(1)) h2=(fun2(end)-fun2(1))/(freq(end)-freq(1)) h3=(fun3(end)-fun3(1))/(freq(end)-freq(1)) h4=(fun4(end)-fun4(1))/(freq(end)-freq(1))

%calculating omega in J omeg1J=-interp1(freq,fun1,0,'pchip') omeg2J=-interp1(freq,fun2,0,'pchip') omeg3J=-interp1(freq,fun3,0,'pchip') omeg4J=-interp1(freq,fun4,0,'pchip')

%calculating omega in eV omeg1eV=-interp1(freq,fun1,0,'pchip')/ev omeg2eV=-interp1(freq,fun2,0,'pchip')/ev omeg3eV=-interp1(freq,fun3,0,'pchip')/ev omeg4eV=-interp1(freq,fun4,0,'pchip')/ev

%% Error Analysis

% error for eV from least squares fits coefficients h and omeg sigmay1=sqrt((1/15)*sum((data1-(h1*freq)+omeg1J).^2)) sigmay2=sqrt((1/15)*sum((data2-(h2*freq)+omeg2J).^2)) sigmay3=sqrt((1/15)*sum((data3-(h3*freq)+omeg3J).^2)) sigmay4=sqrt((1/15)*sum((data4-(h4*freq)+omeg4J).^2))

Delta=(5*sum(freq.^2))-(sum(freq)^2)

% calculating stdm for h and omega sigmah1=sigmay1*sqrt(5/Delta) sigmah2=sigmay2*sqrt(5/Delta) sigmah3=sigmay3*sqrt(5/Delta) sigmah4=sigmay4*sqrt(5/Delta) sigmaoeV1=sigmay1*sqrt(sum(freq.^2)/Delta)/ev sigmaoeV2=sigmay2*sqrt(sum(freq.^2)/Delta)/ev sigmaoeV3=sigmay3*sqrt(sum(freq.^2)/Delta)/ev sigmaoeV4=sigmay4*sqrt(sum(freq.^2)/Delta)/ev

% average h and omega with their average stdms Havg=(h1+h2+h3+h4)/4 STDMH=(sigmah1+sigmah2+sigmah3+sigmah4)/4 OMEGavg=(omeg1eV+omeg2eV+omeg3eV+omeg4eV)/4 STDMOMEG=(sigmaoeV1+sigmaoeV2+sigmaoeV3+sigmaoeV4)/4

%% Extra Formal Report Measurements freq = [5.18672E14, 5.48896E14, 6.87858E14, 7.40858E14, 8.20264E14]; newdata1=[.713 .845 1.488 1.669 2.009] newdata2=[.710 .841 1.480 1.705 2.045] newdata20=[.707 .840 1.480 1.696 2.035] newdata60=[.707 .842 1.481 1.704 2.035]

ev = 1.602E-19; %electron charge. newdata1 = newdata1 .* ev; newdata2 = newdata2 .* ev; newdata20 = newdata20 .* ev; newdata60 = newdata60 .* ev;

% least squares fitting newpoly1=polyfit(freq, newdata1, 1) newfun1=polyval(newpoly1,freq); newpoly2=polyfit(freq, newdata2, 1) newfun2=polyval(newpoly2,freq); newpoly20=polyfit(freq, newdata20, 1) newfun20=polyval(newpoly20,freq); newpoly60=polyfit(freq, newdata60, 1) newfun60=polyval(newpoly60,freq);

% plots figure(4); subplot(2,2,1); scatter(freq, newdata1); hold on, plot(freq, newfun1,'color','red');... title('Run1, 100% intensity'),xlabel('fq(Hz)'),ylabel('V'), hold off subplot(2,2,2); scatter(freq, newdata2); hold on, plot(freq, newfun2,'color','red');... title('Run2, 100% intensity'),xlabel('fq(Hz)'),ylabel('V'), hold off subplot(2,2,3); scatter(freq, newdata20); hold on, plot(freq, newfun20,'color','red');... title('Run3, 20% intensity'),xlabel('fq(Hz)'),ylabel('V'), hold off subplot(2,2,4); scatter(freq, newdata60); hold on, plot(freq, newfun60,'color','red');... title('Run4, 60% intensity'),xlabel('fq(Hz)'),ylabel('V'), hold off

% calculating h h1f=(newfun1(end)-newfun1(1))/(freq(end)-freq(1)) h2f=(newfun2(end)-newfun2(1))/(freq(end)-freq(1)) h20f=(newfun20(end)-newfun20(1))/(freq(end)-freq(1)) h60f=(newfun60(end)-newfun60(1))/(freq(end)-freq(1))

% calculating w omeg1Jf=-interp1(freq,newfun1,0,'pchip'); omeg2Jf=-interp1(freq,newfun2,0,'pchip'); omeg20Jf=-interp1(freq,newfun20,0,'pchip'); omeg60Jf=-interp1(freq,newfun60,0,'pchip');

% error for eV from least squares fits coefficients h and omeg sigmay1f=sqrt((1/15)*sum((newdata1-(h1f*freq)+omeg1Jf).^2)); sigmay2f=sqrt((1/15)*sum((newdata2-(h2f*freq)+omeg2Jf).^2)); sigmay20f=sqrt((1/15)*sum((newdata20-(h20f*freq)+omeg20Jf).^2)); sigmay60f=sqrt((1/15)*sum((newdata60-(h60f*freq)+omeg60Jf).^2));

Delta=(5*sum(freq.^2))-(sum(freq)^2);

% calculating stdm for h and omega sigmah1f=sigmay1f*sqrt(5/Delta) sigmah2f=sigmay2f*sqrt(5/Delta) sigmah20f=sigmay20f*sqrt(5/Delta) sigmah60f=sigmay60f*sqrt(5/Delta)

STDMHf=(sigmah1f+sigmah2f+sigmah20f+sigmah60f)/4