Optics: Transmitted Angle, Critical Angle
Formulas Used
Reflected Angle: θr =
θ
Transmitted Angel: θt
= asin((n1 * sin θ)/n2)
Critical Angle: θc =
asin(n1/n2), n2 > n1
Perpendicular Frensel Parameters (t, r):
t = (2 * n1 * cos θ) / (n1 * cos θ + n2 * cos θt)
r = (n1 * cos θ – n2 * cos θt) / (n1 * cos θ + n2 * cos θt)
Parallel Fresnel Parameters (t, r):
t = (2 * n1 * cos θ) / (n1 * cos θt + n2 * cos θ)
r = (n1 * cos θt – n2 * cos θ) / (n1 * cos θt + n2 * cos θ)
Table of Indices of Reflection (n)
|
Air
|
1.00
|
Moissanite (SiC)
|
2.65
|
|
Carbon Dioxide (CO2)
|
1.0045
|
Pyrex
|
1.47
|
|
Cubic Zirconia
|
2.15
|
Salt (NaCl)
|
1.54
|
|
Diamond
|
2.42
|
Sapphire
|
1.76
|
|
Glass
|
1.52
|
Silicon
|
3.45
|
|
Ice
|
1.31
|
Water
|
1.33
|
HP Prime Program FLATOPTIC
EXPORT
FLATOPTIC()
BEGIN
// 2017-12-17 EWS
// Solar Energy
// Change to degree
HAngle:=1;
// index of refraction
LOCAL L0:={1,1.0045,2.15,2.42,
1.52,1.31,2.65,1.47,
1.54,1.76,3.45,1.33};
LOCAL L1:={"Air","CO2",
"Cubic
Zirconia","Diamond",
"Glass","Ice",
"Moissanite
(SiC)","Pyrex",
"Salt (NaCl)","Sapphire",
"Silicon","Water"};
LOCAL L2:={"Perpendicular",
"Parallel",
"None"};
LOCAL n1,n2,k1,k2,θ,t,r;
LOCAL θc,θt,θr,x;
INPUT({{k1,L1},{k2,L1},θ,{x,L2}},
"Optic - Flat Interface",
{"Medium 1: ","Medium 2:
",
"Angle (°):
","Polarized?"}
);
// Calculation
PRINT();
θr:=θ;
PRINT("Reflect Angle:
"+θr+"°");
n1:=L0(k1); n2:=L0(k2);
IF n2>n1 THEN
θc:=ASIN(n1/n2);
PRINT("Critical Angle:
"+θc+"°");
END;
θt:=ASIN(n1*SIN(θ)/n2);
PRINT("Transmitted Angle: "+
θt+"°");
IF x==1 THEN
t:=(2*n1*COS(θ))/
(n1*COS(θ)+n2*COS(θt));
r:=(n1*COS(θ)-n2*COS(θt))/
(n1*COS(θ)+n2*COS(θt));
PRINT("t: "+t);
PRINT("r: "+r);
END;
IF x==2 THEN
t:=(2*n1*COS(θ))/
(n1*COS(θt)+n2*COS(θ));
r:=(n1*COS(θt)-n2*COS(θ))/
(n1*COS(θt)+n2*COS(θ));
PRINT("t: "+t);
PRINT("r: "+r);
END;
END;
TI-84 Plus CE Program
"EWS
2017-12-17"
{1,1.0045,2.15,2.42,1.52,1.31,2.65,1.47,1.54,1.76,3.45,1.33}→L6
Degree
For(K,1,2)
Disp "1. AIR 2.
CO2 3. CUB.ZIC.","4. DIAMOND 5. GLASS 6. ICE","7.
MOISANITE","8. PYREX 9. NACL","10. SAPPHIRE 11.
SIL.","12. WATER"
Input M
If K=1:M→N
End
L6(N)→N:L6(M)→M
Input
"INCIDENT: °",θ
sin^-1(N*sin(θ)/M)→A
Disp
"TRANSMITED: °",A
If M>N:Then
sin^-1(N/M)→C
Disp "CRITICAL:
°",C
End
Pause
Menu("POLARISE?","PERPENDICULAR",1,"PARALLEL",2,"NONE",3)
Lbl 1
(2Ncos(θ))/(Ncos(θ)+Mcos(A))→T
(Ncos(θ)-Mcos(T))/(Ncos(θ)+Mcos(T))→R
Disp
"T",T,"R",R
Goto 3
Lbl 2
(2Ncos(θ))/(Ncos(T)+Mcos(θ))→T
(Ncos(T)-Mcos(θ))/(Ncos(T)+Mcos(θ))→R
Disp
"T",T,"R",R
Lbl 3
Source:
Klaus Jäger,
Olindo Isabella, Arno H.M. Smets, René
A.C.M.M. van Swaaij, Miro Zeeman Solar
Energy: Fundamental, Technology, and Systems Delft University of Technology, 2014
(no money is made from this blog entry)
Hopefully you find this useful.
Eddie
This blog is property of Edward Shore, 2017
