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 Date 08/09/2010
Script S3_2_1A.m
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%==============================================
%Natural lightA - values at the UPPER SURFACE
%due to reflection and refraction
%==============================================
%
%the refractive index above the upper surface
n1=1;
%and below the upper surface
n2=1.6;
%==============================================
%
%we are in the Brewster situation
%the angle of incidence, in radian,is
ti=atan(n2/n1);
%and in degree
tig=ti*(180/pi)
%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
%
%for natural light we assume gamma = 45°
%then the corresponding square of the
%functions sine and cosine is 0.5
%reflexivity R (see pag. 113)
R=0.5*(IRw+IRy)
%refractivity T (see pag. 113)
T=0.5*(ITw+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
%==============================================
%
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Script S3_2_1B.m
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%==============================================
%Natural lightB - values at the LOWER SURFACE
%due to reflection and refraction
%==============================================
%
%the refractive index above the LOWER surface
n1=1.6;
%and below the LOWER surface
n2=1;
%==============================================
%
%the angle of incidence, in degree, is NOW EQUAL to the
%previous angle of refraction at the UPPER surface
tig=32.0054
%and 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
%
%for natural light we assume gamma = 45°
%then the corresponding square of the
%functions sine and cosine is 0.5
%reflexivity R (see pag. 113)
R=0.5*(IRw+IRy)
%refractivity T (see pag. 113)
T=0.5*(ITw+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
%pag. 125, second row
%"principle of (not if) conservation"
%==============================================
%==============================================

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