| Date 08/09/2010 |
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| Script S5_2_14.m | |||
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%=============================================
%Grating 3 %============================================= % %the two wavelengths in microns lambda1=0.58900; lambda2=0.58958; %N is defined applying the Rayleigh criterion with m = 1 Rayl=lambda1/(lambda2-lambda1); N=ceil(Rayl) %distance d between the slits %and their widths h are in microns d=6; h=2; %angular positions teta1 in degrees and in radians teta1g=5:0.0001:6; %!!! %a very great number of elements is necessary %for the array teta1g and for the next related arrays %!!! Mteta1=length(teta1g); teta1=teta1g*(pi/180); % %============================================= %the square of the formula sin(alfa)/alfa %============================================= % fatth=(pi*h)*sin(teta1); alfa1=fatth./lambda1; alfa2=fatth./lambda2; coef1n=sin(alfa1).^2; coef2n=sin(alfa2).^2; coef1d=alfa1.^2; coef2d=alfa2.^2; difr1=coef1n./coef1d; difr2=coef2n./coef2d; % %============================================= %the square of the formula sin(Nbeta)/(Nsen(beta)) %============================================= % fattd=(pi*d)*sin(teta1); beta1=fattd./lambda1; beta2=fattd./lambda2; arg1=N*beta1; arg2=N*beta2; num1=sin(arg1); num2=sin(arg2); den1=N*sin(beta1); den2=N*sin(beta2); % Int1=num1./den1; Int2=num2./den2; % Intr1=Int1.^2; Intr2=Int2.^2; % %============================================= %relative intensity Ir1 and Ir2 for the two %lines of the first order and their sum %============================================= % Ir1=difr1.*Intr1; Ir2=difr2.*Intr2; Ir=Ir1+Ir2; %corresponding plots plot(teta1g,Ir1,'r-',teta1g,Ir2,'b-',teta1g,Ir,'g-') title('Ir1 (red for lambda1), Ir2 (blue for lambda2), Ir (green for their sum)') % %!!! a very narrow interval of angles is used in the plot!!! axis([5.628 5.645 0 0.7]) % %============================================= %maxima of Ir1, Ir2, their positions into the %arrays, their angular positions %============================================= % %maxima and their positions into the arrays Ir1 and Ir2 [maxIr1,indmax1]=max(Ir1) [maxIr2,indmax2]=max(Ir2) %corresponding angular positions for the maxima angmax1=teta1g(indmax1) angmax2=teta1g(indmax2) %for the saddle point part of the array Ir is used Irsaddle=Ir(indmax1:indmax2); [minS,indS]=min(Irsaddle) %indS is the position from indmax1!!! %corresponding angular position of the saddle point teta1S=teta1g(indmax1:indmax2); angS=teta1S(indS); % %============================================= %check of the ratio of intensities for the %saddle point with expected value 8/(pi^2) %============================================= % %the ratio between minS and maxIr1 or maxIr2 saddle1=minS/maxIr1 check=8/(pi^2) %================================================= %check of position of the minimum of Ir2 to the %left of its maximum %================================================= % %we search the position ind2p into the array Ir2 %of first secondary maximum of Ir2 (to the left of the primary maximum) %between the elements 1 and indmax1 Ir2p=Ir2(1:indmax1); [max2p,ind2p]=max(Ir2p); %and corresponding angular position teta12pg teta12p=teta1g(1:indmax1); teta12pg=teta12p(ind2p); %we search the position of the second minimum of Ir2 %next to its primary maximum %part of the array Ir2 between ind2p and ind2pS=indmax1+indS ind2pS=indmax1+indS; Ir22=Ir2(ind2p:ind2pS); [min2L,ind2L]=min(Ir22); %ind2L is the position from ind2p %its position from the beginning is indmin2=ind2L+ind2p % %corresponding angle angmin2=teta1g(indmin2) % %================================================= %check of position of the minimum of Ir1 to the %right of its maximum %================================================= % %it is used part of Ir1 between position ind2pS %(that of the saddle point from the beginning) %and ind1S=indmax2+indS %the extension of indS to indmax2 is reasonable ind1S=indmax2+indS; Ir11=Ir1(ind2pS:ind1S); [min11,indmin11]=min(Ir11); %indmin1 is the position from ind2pS %its position from the beginning is indmin1=ind2pS+indmin11 %corresponding angle is angmin1=teta1g(indmin1) %================================================= % |
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