| Date 08/09/2010 |
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| Script S1_2_14.m | |||
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%==============================================
%refraction through a transparent plate whose %refractive index is a linear function od the %thickness h %============================================== % %thickness h in cm h=1; %refractive index and h are divided in N parts N=100; %the first and the last term of refractive index n1=1.45; n2=2.50; %value z of a part of h (called deltah in the book) z=h/N; %the range of refractive indexes n=linspace(n1,n2,N); %the angle on incidence in degrees between 0 and 60 alfag=eps:2:60 %the number of angles maxj=length(alfag); % %================================================ %the external loop varying alfag %================================================ % for j=1:maxj alfa=alfag(j)*pi/180; arg(1)=sin(alfa)/n(1); beta(1)=asin(arg(1)); %the first shift x x(1)=z*tan(beta(1)); h=x(1); %the first length b b(1)=z/cos(beta(1)); arg1(1)=alfa-beta(1); %the first distance d d=b(1)*sin(arg1(1)); % %================================== %the inner loop over the N slots %================================== % for i=2:N arg(i)=n(i-1)*sin(beta(i-1))/n(i); beta(i)=asin(arg(i)); %next shift x x(i)=z*tan(beta(i)); h=h+x(i); %next length b b(i)=z/cos(beta(i)); arg1(i)=beta(i-1)-beta(i); %next distance d d=d+b(i)*sin(arg1(i)); end % %================================== %end of the inner loop %================================== % %an element is added to the array H H(j)=h; %and to the array D D(j)=d; end % %================================================ %end of the external loop %================================================ % %the array H contains vertical partial shifts xi, in cm, %varying the angle of incidence H; %the array D contains partial distances di, in cm, %varying the angle of incidence D; % %================================================ % %================================================ % %the refractive index is fixed An=1.45; %the thickness of the plate in cm Ah=1; %the angle of incidence varying from 0 to 60° Aalfag=eps:2:60; %the angles in radians Aalfa=Aalfag*pi/180 %the refraction angle Aarg=sin(Aalfa)/An; Abeta=(asin(Aarg)); %=============================================================== %we check that the emerging angle is equal to the incident angle Atest=asin(An*sin(Abeta)) %=============================================================== %the vertical shift Ax in cm varying the angle of incidence Ax=Ah*tan(Abeta) Ab=Ah./cos(Abeta); Aarg1=Aalfa-Abeta; %the distance Ad between the incident and the emerging rays Ad=Ab.*sin(Aarg1) % %========================================================================== %plot of vertical shift with n variable and constant %========================================================================== plot(alfag,H,'bd-',Aalfag,Ax,'ro-'),grid on, title('blue for n variabile and red for n constant'), xlabel('angle of incidence in degree') ylabel('vertical shifts in cm') % axis([0 90 0 1] figure % %========================================================================== %plot of the distance between the incident and the emerging rays %with n variable and constant %========================================================================== subplot(2,1,1) plot(alfag,D,'bd-'),grid on, title('the distance for n variable varying alfa'), % axis([0 90 0 1] subplot(2,1,2) plot(Aalfag,Ad,'ro-'),grid on, title('the distance for n constant varying alfa') % axis([0 90 0 1] %========================================================================== % |
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