(*^
::[	Information =

	"This is a Mathematica Notebook file.  It contains ASCII text, and can be
	transferred by email, ftp, or other text-file transfer utility.  It should
	be read or edited using a copy of Mathematica or MathReader.  If you 
	received this as email, use your mail application or copy/paste to save 
	everything from the line containing (*^ down to the line containing ^*)
	into a plain text file.  On some systems you may have to give the file a 
	name ending with ".ma" to allow Mathematica to recognize it as a Notebook.
	The line below identifies what version of Mathematica created this file,
	but it can be opened using any other version as well.";

	FrontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.2";

	MacintoshStandardFontEncoding; 
	
	fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8,  24, "Times"; 
	fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6,  18, "Times"; 
	fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6,  14, "Times"; 
	fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20,  18, "Times"; 
	fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15,  14, "Times"; 
	fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12,  12, "Times"; 
	fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  10, "Times"; 
	fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-5,  12, "Courier"; 
	fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5,  12, "Courier"; 
	fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5,  12, "Courier"; 
	fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5,  12, "Courier"; 
	fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B65535, L-5,  12, "Courier"; 
	fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287,  12, "Courier"; 
	fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic,  10, "Geneva"; 
	fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = leftheader, inactive, L2,  12, "Times"; 
	fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7,  12, "Times"; 
	fontset = leftfooter, inactive, L2,  12, "Times"; 
	fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  10, "Times"; 
	fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	paletteColors = 128; automaticGrouping; currentKernel; 
]
:[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-
^*)
