Friday, December 22, 2017

Optics: Transmitted Angle, Critical Angle

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

1 comment:

  1. This problem is interesting. It zaps the reader back in time when Snellius, Fermat, Bernouilli analyzed this 'trivial' phenomena.

    ReplyDelete

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