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 Date 06/09/2010
Script S3_2_2A.m
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%==============================================
%Linearly polarized lightA
%values at the upper surface B
%due to reflection and refraction
%Attention! One only value of tig and
%only one value of gamma must be made "uncomment"
%and the other values must be made "comment"
%
%THIS SCRIPT IS USED ASSUMING DIFFERENT COUPLE
%OF THE ANGLES tig AND gamma
%==============================================
%
%the refractive index above the LOWER surface
n1=1;
%and below the LOWER surface
n2=1.5;
%==============================================
%
%the angle of incidence, in degree, is equal
%alternatively to 40°, the Brewster angle and to 70°
%first angle of incidence 40°
% tig=40;
%second angle (Brewster) of incidence
tig=(atan(n2/n1))*180/pi
%third angle of incidence 70°
% tig=70;
%the same angle in radian
ti=tig*pi/180;
%the corresponding angle of refraction in radian
tt=asin((n1/n2)*sin(ti));
%and in degree
ttg=tt*180/pi
%============================================
%for following names of variables
%IRw IRy ITw and ITy
%I means a relative intensity
%R and T denotes reflected and refracted ray
%w/y the component parallel/normal to the plane of incidence
%=========================================================
%
%We calculate IRw IRy ITw and ITy
%relative intensity of the components of the electric field
%parallel/normal to the plane of incidence
%for the reflected and refracted ray
%preliminary calculus
sum=ti+tt;
dif=ti-tt;
numr1wp=tan(dif)^2;
denr1w=tan(sum)^2;
numr1yp=sin(dif)^2;
denr1y=sin(sum)^2;
numt2wy=sin(2*tt)*sin(2*ti);
dent1w=(sin(sum)*cos(dif))^2;
dent1y=(sin(sum))^2;
%the four relative intensities
IRw=numr1wp/denr1w
IRy=numr1yp/denr1y
ITw=numt2wy/dent1w
ITy=numt2wy/dent1y
%we check the sum of parallel intensities
checkw=IRw+ITw
%and the sum of normal intensities
checky=IRy+ITy
%
%first we assume gamma = 0°
gamma=0;
%then gamma = 90°
% gamma=pi/2;
a=cos(gamma)^2
b=sin(gamma)^2
%reflexivity R (see pag. 113)
R=a*IRw+b*IRy
%refractivity T (see pag. 113)
T=a*ITw+b*ITy
%we check the sum of reflexivity and refractivity
checkRT=R+T
%values of degree of polarization
num11=abs(IRw-IRy)
den11=abs(IRw+IRy)
%of reflected ray
Pr=num11/den11
num22=abs(ITw-ITy)
den22=abs(ITy+ITy)
%and refracted ray
Pt=num22/den22
%==============================================
%
%==============================================
%==============================================
%Corrigenda
%see Tabble 3.1, pag. 126
%The right value of Pt is 0.1 rather than 0.01
%==============================================
%==============================================

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Script S3_2_2B.m
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%==============================================
%Linearly polarized lightB
%values at the upper surface B due to reflection
%and refraction. One only value of tig and one
%of gamma are used
%==============================================
%
%the refractive index above the LOWER surface
n1=1;
%and below the LOWER surface
n2=1.5;
%==============================================
%
%the angle of incidence, in degree,
tig=75;
%the same angle in radian
ti=tig*pi/180;
%the corresponding angle of refraction in radian
tt=asin((n1/n2)*sin(ti));
%and in degree
ttg=tt*180/pi
%============================================
%for following names of variables
%IRw IRy ITw and ITy
%I means a relative intensity
%R and T denotes reflected and refracted ray
%w/y the component parallel/normal to the plane of incidence
%=========================================================
%
%We calculate IRw IRy ITw and ITy
%relative intensity of the components of the electric field
%parallel/normal to the plane of incidence
%for the reflected and refracted ray
%preliminary calculus
sum=ti+tt;
dif=ti-tt;
numr1wp=tan(dif)^2;
denr1w=tan(sum)^2;
numr1yp=sin(dif)^2;
denr1y=sin(sum)^2;
numt2wy=sin(2*tt)*sin(2*ti);
dent1w=(sin(sum)*cos(dif))^2;
dent1y=(sin(sum))^2;
%the four relative intensities
IRw=numr1wp/denr1w
IRy=numr1yp/denr1y
ITw=numt2wy/dent1w
ITy=numt2wy/dent1y
%we check the sum of parallel intensities
checkw=IRw+ITw
%and the sum of normal intensities
checky=IRy+ITy
%
%gamma is defined in the interval 0-180°
gamma=linspace(0,pi,50);
gammag=gamma*180/pi;
a=cos(gamma).^2
b=sin(gamma).^2
%reflexivity R (see pag. 113)
R=a*IRw+b*IRy
%refractivity T (see pag. 113)
T=a*ITw+b*ITy
%we check the sum of reflexivity and refractivity
checkRT=R+T
%plot of R and T for tig = 70° varying gammag 0° to 180°
plot(gammag,R,'r-o',gammag,T,'b-d'),grid on
title('R(red) and T(blue) for tig = 70° varying gammag from 0° to 180°')
%==============================================
%
%==============================================
%==============================================
%Corrigenda
%in the third row of pag.127 "value 70°" must
%be changed in "value 75°"
%==============================================
%==============================================

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