(*^
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:[font = title; inactive; preserveAspect; startGroup]
Reflected_intensity.m
:[font = section; inactive; preserveAspect; startGroup]
Calculation of the reflected intensity from a smooth dielectric surface with refractive index, n
:[font = input; preserveAspect; startGroup]
n=1.333
:[font = output; output; inactive; preserveAspect; endGroup]
1.333
;[o]
1.333
:[font = text; inactive; preserveAspect]
Number of plot points in 3D plots
:[font = input; preserveAspect; startGroup]
pp=10
:[font = output; output; inactive; preserveAspect; endGroup]
10
;[o]
10
:[font = subsection; inactive; preserveAspect; startGroup]
Definition of the angle of incidence, i, as a function of the 'altitude' angle in the 3D plot
:[font = input; preserveAspect]
i[u_]:= Pi/4-u/2
:[font = input; preserveAspect; startGroup]
Plot[i[u],{u,-Pi/2,Pi/2}]
:[font = output; output; inactive; preserveAspect; endGroup; endGroup]
Graphics["<<>>"]
;[o]
-Graphics-
:[font = subsection; inactive; preserveAspect; startGroup]
Definition of the angle of refraction, r, using Snell's law
:[font = input; preserveAspect]
r[u_]:= ArcSin[Sin[i[u]]/n]
:[font = input; preserveAspect; startGroup]
Plot[r[u],{u,-Pi/2,Pi/2}]
:[font = output; output; inactive; preserveAspect; endGroup; endGroup]
Graphics["<<>>"]
;[o]
-Graphics-
:[font = subsection; inactive; preserveAspect; startGroup]
Intensity of reflection with the E-vector perpendicular to the plane containing the incident and reflected rays
:[font = input; preserveAspect]
iperp[u_]:= (Sin[i[u]-r[u]]/Sin[i[u]+r[u]])^2
:[font = input; preserveAspect; startGroup]
Plot[iperp[u], {u,-Pi/2,1.57}]
:[font = output; output; inactive; preserveAspect; endGroup; endGroup]
Graphics["<<>>"]
;[o]
-Graphics-
:[font = subsection; inactive; preserveAspect; startGroup]
Intensity of reflection with the E-vector in the plane containing the incident and reflected rays
:[font = input; preserveAspect]
ipar[u_]:= (Tan[i[u]-r[u]]/Tan[i[u]+r[u]])^2
:[font = input; preserveAspect; startGroup]
Plot[ipar[u], {u,-Pi/2,1.57}]
:[font = output; output; inactive; preserveAspect; endGroup; endGroup]
Graphics["<<>>"]
;[o]
-Graphics-
:[font = subsection; inactive; preserveAspect; startGroup]
Fractional polarization of reflected light
:[font = input; preserveAspect]
prefl[u_]:= (iperp[u]-ipar[u])/(iperp[u]+ipar[u])
:[font = input; preserveAspect; startGroup]
Plot[prefl[u], {u,-Pi/2,1.57}]
:[font = output; output; inactive; preserveAspect; endGroup; endGroup; endGroup]
Graphics["<<>>"]
;[o]
-Graphics-
:[font = section; inactive; preserveAspect; startGroup]
3D plots of the reflected intensity and polarization
:[font = subsection; inactive; preserveAspect; startGroup]
For perpendicular polarization
:[font = input; preserveAspect; startGroup]

ParametricPlot3D[{
iperp[u] Sin[u], 
iperp[u] Cos[t] Cos[u], 
iperp[u] Sin[t] Cos[u]},
{t,-Pi/2,Pi/2}, {u,-Pi/2,1.57},
PlotPoints->pp,
Axes -> True, 
AxesStyle -> Thickness[0.01]]
:[font = output; output; inactive; preserveAspect; endGroup; endGroup]
Graphics3D["<<>>"]
;[o]
-Graphics3D-
:[font = subsection; inactive; preserveAspect; startGroup]
For parallel polarization
:[font = input; preserveAspect; startGroup]

ParametricPlot3D[{
ipar[u] Sin[u], 
ipar[u] Cos[t] Cos[u], 
ipar[u] Sin[t] Cos[u]},
{t,-Pi/2,Pi/2}, {u,-1,1.57},
PlotPoints->pp,
Axes -> True, 
AxesStyle -> Thickness[0.01]]
:[font = output; output; inactive; preserveAspect; endGroup; endGroup]
Graphics3D["<<>>"]
;[o]
-Graphics3D-
:[font = subsection; inactive; preserveAspect; startGroup]
Total intensity
:[font = input; preserveAspect; startGroup]
ParametricPlot3D[{
(ipar[u]+iperp[u]) Sin[u], 
(ipar[u]+iperp[u]) Cos[t] Cos[u], 
(ipar[u]+iperp[u]) Sin[t] Cos[u]},
{t,-Pi/2,Pi/2}, {u,-Pi/2,1.57},
PlotPoints->pp,
Axes -> True, 
AxesStyle -> Thickness[0.01]]
:[font = output; output; inactive; preserveAspect; endGroup; endGroup]
Graphics3D["<<>>"]
;[o]
-Graphics3D-
:[font = subsection; inactive; preserveAspect; startGroup]
Fractional polarization
:[font = input; preserveAspect; startGroup]
ParametricPlot3D[{
prefl[u] Sin[u], 
prefl[u] Cos[t] Cos[u], 
prefl[u] Sin[t] Cos[u]},
{t,-Pi/2,Pi/2}, {u,-Pi/2,1.57},
PlotPoints->pp,
Axes -> True, 
AxesStyle -> Thickness[0.01]]
:[font = output; output; inactive; preserveAspect; endGroup; endGroup; endGroup; endGroup]
Graphics3D["<<>>"]
;[o]
-Graphics3D-
^*)