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
// 20171217 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;
TI84 Plus CE Program
"EWS
20171217"
{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
This problem is interesting. It zaps the reader back in time when Snellius, Fermat, Bernouilli analyzed this 'trivial' phenomena.
ReplyDelete