# waves¶

Hint: Spherical waves

Author: Otto Schaile
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, November 29, 2022 at 11:17 AM.

In [1]:
%%cpp -d
#include "TROOT.h"
#include "TCanvas.h"
#include "TColor.h"
#include "TArc.h"
#include "TGraph.h"
#include "TF2.h"
#include "TLine.h"
#include "TLatex.h"
#include "TMath.h"
#include "TStyle.h"


In [2]:
%%cpp -d
Double_t interference( Double_t *x, Double_t *par)
{
Double_t x_p2 = x[0] * x[0];
Double_t d_2 = 0.5 * par[2];
Double_t ym_p2 = (x[1] - d_2) * (x[1] - d_2);
Double_t yp_p2 = (x[1] + d_2) * (x[1] + d_2);
Double_t  tpi_l = TMath::Pi() /  par[1];
Double_t amplitude = par[0] * (cos(tpi_l  * sqrt(x_p2 + ym_p2))
+ par[3] * cos(tpi_l  * sqrt(x_p2 + yp_p2)));
return amplitude * amplitude;
}


In [3]:
%%cpp -d
Double_t result( Double_t *x, Double_t *par)
{
Double_t xint[2];
Double_t  maxintens = 0, xcur = 14;
Double_t dlambda = 0.1 * par[1];
for(Int_t i=0; i<10; i++){
xint[0] = xcur;
xint[1] = x[1];
Double_t  intens = interference(xint, par);
if(intens > maxintens) maxintens = intens;
xcur -= dlambda;
}
return maxintens;
}


Arguments are defined.

In [4]:
Double_t d = 3;
Double_t lambda = 1;
Double_t amp = 10;

In [5]:
TCanvas *c1 = new TCanvas("waves", "A double slit experiment", 300, 40, 1004, 759);
c1->Range(0, -10,  30, 10);
c1->SetFillColor(0);

const Int_t colNum = 30;
Int_t palette[colNum];
for (Int_t i=0;i<colNum;i++) {
Float_t level = 1.*i/colNum;
palette[i] = TColor::GetColor((Float_t) TMath::Power(level,0.3), (Float_t) TMath::Power(level,0.3), (Float_t) 0.5*level);
// palette[i] = 1001+i;
}
gStyle->SetPalette(colNum, palette);

c1->cd();

TF2 *f0 = new TF2("ray_source",interference, 0.02, 15, -8, 8, 4);
f0->SetParameters(amp, lambda, 0, 0);
f0->SetNpx(200);
f0->SetNpy(200);
f0->SetContour(colNum-2);
f0->Draw("samecol");

TLatex title;
title.DrawLatex(1.6, 8.5, "A double slit experiment");

TGraph *graph = new TGraph(4);
graph->SetFillColor(0);
graph->SetFillStyle(1001);
graph->SetLineWidth(0);
graph->SetPoint(0, 0., 0.1);
graph->SetPoint(1, 14.8, 8);
graph->SetPoint(2, 0, 8);
graph->SetPoint(3, 0, 0.1);
graph->Draw("F");

graph = new TGraph(4);
graph->SetFillColor(0);
graph->SetFillStyle(1001);
graph->SetLineWidth(0);
graph->SetPoint(0, 0, -0.1);
graph->SetPoint(1, 14.8, -8);
graph->SetPoint(2, 0, -8);
graph->SetPoint(3, 0, -0.1);
graph->Draw("F");

TLine * line = new TLine(15,-10, 15, 0 - 0.5*d -0.2);
line->SetLineWidth(10);
line->Draw();

line = new TLine(15, 0 - 0.5*d +0.2 ,15, 0 + 0.5*d -0.2);
line->SetLineWidth(10);
line->Draw();

line = new TLine(15,0 + 0.5*d + 0.2,15, 10);
line->SetLineWidth(10);
line->Draw();

TF2 *finter = new TF2("interference",interference, 0.01, 14, -10, 10, 4);
finter->SetParameters(amp, lambda, d, 1);
finter->SetNpx(200);
finter->SetNpy(200);
finter->SetContour(colNum-2);
finter->Draw("samecol");

TArc arc;
arc.SetFillStyle(0);
arc.SetLineWidth(2);
arc.SetLineColor(5);
Float_t r = 0.5 * lambda, dr = lambda;
for (Int_t i = 0; i < 16; i++) {
arc.DrawArc(0,  0.5*d, r, 0., 360., "only");
arc.DrawArc(0, -0.5*d, r, 0., 360., "only");
r += dr;
}

TF2 *fresult = new TF2("result",result, 14, 15, -10, 10, 4);
fresult->SetParameters(amp, lambda, d, 1);
fresult->SetNpx(300);
fresult->SetNpy(300);
fresult->SetContour(colNum-2);
fresult->Draw("samecol");

line = new TLine(13.8,-10, 14, 10);
line->SetLineWidth(10); line->SetLineColor(0); line->Draw();
c1->Modified(kTRUE);
c1->Update();
c1->SetEditable(kTRUE);


Draw all canvases

In [6]:
gROOT->GetListOfCanvases()->Draw()