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# HP Prime: Law of Refraction

HP Prime: Law of Refraction

Introduction

The program DRAWREFRACT, visually demonstrates the Law of Refraction, or Snell’s Law:

n1 sin θi = n2 sin θt

The program asks for n1, θi, and n2; and calculates θt.  The program draws the incident ray (in red) and the refracted ray (in blue).  The calculator is set to Degrees mode and the Function app.

Note: you can find the angle character ∡, by pressing [SHIFT] [ × ].

HP Prime: Law of Refraction: DRAWREFRACT

Program:
EXPORT DRAWREFRACT(n1,θ1,n2)
BEGIN
// EWS 2018-08-20
// drawing Descates law
HAngle:=1; // Degrees
LOCAL θ2,x1,y1,x2,y2;
LOCAL str1,str2;
// window setup
STARTAPP(“Function”);
STARTVIEW(11,0);  // Decimal zoom
// calculation
θ2:=ASIN(n1*SIN(θ1)/n2);
x1:=RE(16∡(θ1+90));
y1:=IM(16∡(θ1+90));
x2:=RE(16∡(270+θ2));
y2:=IM(16∡(270+θ2));
// plot
RECT();
// draw axis
LINE(0,−16,0,16,0);
LINE(16,0,−16,0,0);
// draw analysis
LINE(0,0,x1,y1,#FF0000h);
LINE(0,0,x2,y2,#0000FFh);
str1:=”n = “+STRING(n1)+
“, θi = “+STRING(θ1);
str2:=”-> n = “+STRING(n2)+
“, θt = “+STRING(θ2);
TEXTOUT(str1,−15,−5,4,#FF0000h);
TEXTOUT(str2,−15,−8,4,#0000FFh);
WAIT(0);
// display home
STARTVIEW(−1);
END;

Example

n1 = 1.001
θ = 34.5°
n2= 1.205

DRAWREFRACT(1.001, 34.5, 1.205)

Result:
θt = 28.0678429359°

Eddie

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