GraphingCalculator 4;
Window 46 7 789 895;
PaneDivider 309;
FontSizes 14;
2D.Scale 0.5 0.5 2 2;
2D.BottomLeft -0.84375 -12.09375;
2D.Axes 0;
2D.GraphPaper 0;
Text "Fraunhofer interference and diffraction patterns from single and double slits.    
References: Bayman & Hammermesh sec. 4.2; Tipler & Mosca sec. 33.5.   

Version 0.2
To do:
(i) Add slits
(ii) Adjust normalization for multiple slits?
(iii) Resolve singularities at multiple slit peaks
(iv) Parameterize wavelength better/differently? 

I0 – single-slit intensity; a – slit width; d – slit separation; L – wavelength (as a multiple of d); D – distance to screen (so tanT=x/D gives the position on the screen corresponding to angle T.   For small angles note sinT = tanT = x/D.)
";
Expr I_0=1,D=10;
Color 5;
MathPaneSlider 5;
Expr a=slider([0,0.25,40]);
Color 6;
MathPaneSlider 5;
Expr d=slider([0,2,40]);
Color 7;
MathPaneSlider 1;
Expr L=slider([0,1,40]);
Text "Phase difference between rays from top and bottom of each slit as a function of screen position (X):";
Color 4;
Expr function(P,X)=2*pi/L*a/D*X;
Text "Phase difference between rays from centers of adjacent slits as a function of screen position (X):";
Color 8;
Expr function(D,X)=2*pi/L*d/D*X;
Text "Intensity for single-slit diffraction pattern:";
Color 5;
Expr function(I_1,X)=I_0*[sin(function(P,X)/2)/[function(P,X)/2]]^2;
Text "Intensity for two-slit interference-diffraction pattern (note how interference term is modulated by the single-slit diffraction pattern):";
Color 6;
Expr function(I_2,X)=4*function(I_1,X)*[cos([function(D,X)/2])]^2;
Text "Intensity for two-slit interference pattern (neglecting diffraction):";
Color 2;
Expr function(I_(2*I),X)=4*I_0*[cos([function(D,X)/2])]^2;
Text "Intensity for m-slit diffraction pattern:";
Color 2;
Expr function(I_N,X,m)=function(I_1,X)*[sin([m*function(D,X)/2])/sin([function(D,X)/2])]^2;
Text "Envelope for m-slit diffraction:";
Expr function(I_E,X,m)=m^2*function(I_1,X);
Text "Location of intensity maxima as a function of position on the screen.    ";
Color 17;
Expr d*x/D=m*L,in(m,set(-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10)),0<y<I_0;
Text "To plot as a function of angle replace x->Dsinx:";
Color 17;
Expr d*sin(x)=m*L,in(m,set(-5,-4,-3,-2,-1,0,1,2,3,4,5)),0<y<I_0;
Color 17;
Expr function(I_1,x);
Color 3;
Expr function(I_2,x);
Color 17;
Expr function(I_(2*I),x);
Color 17;
Expr function(I_N,x,2);
Color 17;
Expr function(I_E,x,2);
Text "Bragg condition.   d is now the interplanar spacing.";
Color 17;
Expr 2*d*sin(x)=m*L,in(m,set(-5,-4,-3,-2,-1,0,1,2,3,4,5)),0<y<I_0;
Text "

Author: David A. Craig <<http://web.lemoyne.edu/~craigda/>";