| Date 06/09/2010 |
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| Script S2_2_21A.m | |||
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%==============================================
%Three coaxial lensesA %============================================== % %============================================== %============================================== %CORRIGENDA %In the last row of text (pag. 105) %change "modification" with "modifications" %============================================== %============================================== % %values to d and y1 are assigned so that teta1 is a paraxial angle (<20° %with an error less than 2%) d=130; z1=-d; y1=10 %teta1 is assumed negative teta1=-y1/d teta1g=teta1*180/pi % %f is defined in the interval 40-90 degrees f1=40:5:90 %number of elements of the array f1 max=length(f1) %an array of max rows and 11 columns is defined; %it will be redefined by the next instructions F=zeros(max,11); % %============================================== %values of z2,z3,z4,teta2g,y2,teta3g,y3,teta4g %are calculated by the next commands for every %of max values of focal lengths for i=1:max f=f1(i); % %the ray crosses the first lens a1=[1 0;1/f 1]; a2=[y1;teta1]; A=a1*a2; %teta2 is calculated teta2=A(2); teta2g=teta2*180/pi; %z2 is point image for the first lens z2=A(1)/A(2); % %the ray goes from the first to the second %teta2 is assumed negative b1=[1 d;0 1]; b2=[y1;-teta2]; B=b1*b2; %y2 is calculated y2=B(1); % %the ray crosses the second lens %teta2 is now positive c1=[1 0;1/f 1]; c2=[y2;teta2]; C=c1*c2; z3=C(1)/C(2); teta3=C(2); teta3g=teta3*180/pi; % %the ray goes from the second to the third %teta3 is assumed negative d1=[1 d;0 1]; d2=[y2;-teta3]; D=d1*d2; y3=D(1); % %%the ray crosses the third lens %teta3 is now positive e1=[1 0;1/f 1]; e2=[y3;teta3]; E=e1*e2; teta4=E(2); %teta4 in degrees teta4g=teta4*180/pi; %the final point image z4=E(1)/E(2); %the previous values are allocated in a row of the array F %the last two values are the final angular and transverse magnifications F(i,:)=[f,z2,z3,z4,teta2g,y2,teta3g,y3,teta4g,teta4g/teta1g,z4/z1]; end %the array F is now full F % %plot of the point images after first(red circle)-second(blue diamond)- %third(magenta square) lens varying the focal length plot(f1,F(:,2),'ro-',f1,F(:,3),'bd-',f1,F(:,4),'ms-'),grid on title('images after first(red circle) second(blue diamond) third(magenta square) lens varying f') axis([59 71 -50 200]) %============================================== % |
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| Script S2_2_21B.m | |||
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%==============================================
%Three coaxial lensesB %============================================== % %standard formulae are used in a recursive way %the initial distance d of the object from the first lens d=130; %N is the number of the lenses used N=3; f=[60,65,70]; %m is the number of the focal lengths m=length(f); for i=1:m; %for assigned focal length i a=0; %for assigned lens j for j=1:N; z1(i,j)=a-d; z2(i,j)=(f(i)*z1(i,j))/(f(i)+z1(i,j)); a=z2(i,j); end %all lenses are considered end %all focal lengths are considered %============================================== % %z1 is an array of m (number of f) rows and N (number of lenses) columns %containing in each row the distances of point objects for each lens z1 %z2 is an array of m (number of f) rows and N (number of lenses) columns %containing in each row the distances of point images for each lens z2 %F60 is an array of two rows and three columns %first row contains the objects distances when f = 60 %the second row contains the images distances when f = 60 F60=[z1(1,:);z2(1,:)] %and so when f = 65 F65=[z1(2,:);z2(2,:)] %or f = 70 F70=[z1(3,:);z2(3,:)] %plot of the point images after first(red diamond)-second(blue asterisk)- %third(magenta circle) lens varying the focal length plot(f,z2(:,1),'rd-',f,z2(:,2),'b-*',f,z2(:,3),'m-o'),grid on title('images after first(red diamond) second(blue asterisk) third(magenta circle) lens varying f') axis([59 71 -50 200]) %================================================== % |
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