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Happy New Year 2018!

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Eddie

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