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## Beginner's help for a graphic for a free physics textbook

 From: Christoph Schiller Subject: Beginner's help for a graphic for a free physics textbook Date: Tue, 31 Mar 2009 17:33:15 +0200

```With permission form the original author I would like to produce an
improved version of the animated graphic shown at
http://en.wikipedia.org/wiki/File:Snells_law_wavefronts.gif

```
I'd like to add the animation to my 1600 page physics textbook in pdf format
```that I offer on the internet for free.
The original graphics was made in MATLAB (the code is given below.)

just to produce this graphic. So I have a few questions (I have never
used either Octave nor MATLAB):

1 - Does the code shown below run on Octave?
```
2 - How do I input a command file in Octave? (I did not find this in the help files) 3 - Will I be able to produce and save the gif on OSX or do I need other packages?
```
(Here is what I plan to change in the graphics of Snell's law:
- introduce a shaded region in blue to show where the water is
- take out the grey line (becomes unnecessary)
- make the blue lines green (to contrast with the blue water)
```
- make the wave front lines half the thickness they are now (will be more pretty)
```)

```
Any help will be appreciated by the readers world-wide - thank you in advance!
```
Best regards

Christoph Schiller
The free physics textbook
www.motionmountain.net

P.S. Here is the original, unmodified code:

% Illustration of Snell's law
function main()

% indexes of refraction
n1=1.0;
n2=1.5;

sign = -1;% is the source up or down?
O=[0, -1*sign];
k=500;

% KSmrq's colors
red    = [0.867 0.06 0.14];
blue   = [0, 129, 205]/256;
green  = [0, 200,  70]/256;
yellow = [254, 194,   0]/256;
white = 0.99*[1, 1, 1];
black = [0, 0, 0];
gray = 0.5*white;

color1=red;
color2=blue;
color3=gray;
lw = 3;

plot_line=0;
Theta=linspace(0, 2*pi, k);
V=0*Theta; W=0*Theta;
S0=7;
spacing=0.45;
p=floor(S0/spacing);
S=linspace(0, S0, p+1);
spacing=S(2)-S(1);

num_frames = 10;
for frame_iter=1:num_frames

figure(1); clf; hold on; axis equal; axis off;

% plot the interface between diellectrics
L=1.2*S0;
plot([-L, L], [0, 0], 'color', color3, 'linewidth', lw);

% plot a ray
plot_line=1;
s=L;
theta=pi/3; wfr(s, theta, n1, n2, O, sign, plot_line, color1, lw);

% plot the wafefronts
plot_line=0;
for i=1:p

s=S(i)+spacing*(frame_iter-1)/num_frames;

for j=1:k
theta=Theta(j);
```
[V(j), W(j)]=wfr(s, theta, n1, n2, O, sign, plot_line, color1,
```lw);
end
plot(V, W, 'color', color2, 'linewidth', lw);
end

%  dummy points to enlarge the bounding box
plot(0, S0+2.5*spacing, '*', 'color', white);
plot(0, -(S0+2.5*spacing)/n2, '*', 'color', white);

% to know where to crop later
Lx=3.2; Ly=Lx; shift = 1;
plot([-Lx, Lx, Lx, -Lx -Lx], ...
[-Ly, -Ly, Ly, Ly, -Ly]+shift);

file = sprintf('Frame%d.eps', 1000+frame_iter);
disp(file);
saveas(gcf, file, 'psc2')
end

% Converted to gif with the UNIX command
% convert -density 100 -antialias Frame10* Snell_animation.gif
% then cropped in Gimp

function [a, b]=wfr(s, theta, n1, n2, O, sign, plot_line, color1, lw);

X=O+s*[sin(theta), sign*cos(theta)];

if( sign*X(2) > 0 )
t=-sign*O(2)/cos(theta);
X0=O+t*[sin(theta), sign*cos(theta)];

if (plot_line == 1)
```
plot([O(1), X0(1)], [O(2), X0(2)], 'color', color1, 'linewidth', lw,
```'linestyle', '--');
end

d = norm(O-X0);
r = (s-d)*(n2/n1)^(sign);

theta2=asin(n1*sin(theta)/n2);
XE=X0+r*[sin(theta2), sign*cos(theta2)];
else
XE = X;
end
a = XE(1);
b = XE(2);

if (plot_line==1)
```
plot([X0(1), XE(1)], [X0(2), XE(2)], 'color', color1, 'linewidth', lw,
```'linestyle', '--');
end

```