Optics: Transmitted Angle, Critical Angle
12-23-2017, 12:42 AM
Post: #1
 Eddie W. Shore Senior Member Posts: 792 Joined: Dec 2013
Optics: Transmitted Angle, Critical Angle
Original Post (for a table of indices of reflection: http://edspi31415.blogspot.com/2017/12/o...angle.html)

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)

HP Prime Program FLATOPTIC
Code:
 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;
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