Notebook

Initializing the program

To initialize the visualization, you may need to click "Run all initialization cells" above (see button location in figure).

You should see the visualization directly below this line, before the next section.

In [21]:

#This code was authored by Alex Shvonski, Copyright 2020 MIT All Rights Reserved.

%matplotlib notebook
import ipywidgets as widgets
from IPython.display import display, clear_output
from ipywidgets import interact, interactive, interactive_output, fixed, FloatRangeSlider, IntSlider, HBox, Layout, Output, VBox
import numpy as np
import matplotlib.pyplot as plt
from math import pi
import cmath
#import warnings
#warnings.filterwarnings('ignore')

In [22]:

#Define functions
###############################################
###############################################
def intensity(y,d,lam,L):
    #let c*epsilon_0*E_0^2 = 1
    #result = np.cos(pi*d*10**(-3)*y/(lam*10**(-6)*L*10**(3.)))**2.
    result = np.sin(pi*d*10**(-3)*y/(lam*10**(-6)*L*10**(3.)))**2./(pi*d*10**(-3)*y/(lam*10**(-6)*L*10**(3.)))**2.
    return result

In [23]:

#Define plot
###############################################
###############################################
fig, ax = plt.subplots(1, 1, figsize=(9.5, 5))
plt.subplots_adjust(left=0.05, bottom=None, right=1, top=None, wspace=None, hspace=1.)
y_array = np.linspace(-50., 50., 1000)
d = 10. #um = 10^-3 mm
lam = 500 #nm = 10^-6 mm
L = 0.5 #m = 10^3 mm
#############################
#plot1

line_1, = ax.plot(y_array, intensity(y_array,d,lam,L),'r-', lw=2)


#plot params
ax.set_title('Single Slit Diffraction Intensity', fontsize=16)
ax.set_xlabel('$y\,[\mathrm{mm}]$', fontsize=16)
ax.set_xlim(min(y_array),max(y_array))
#ax.axis('off')
ax.set_ylim(0,1)

ax.grid(True)
plt.setp(ax.get_xticklabels(), fontsize=14)
plt.setp(ax.get_yticklabels(), fontsize=14)
    

#Define plot updater
###############################################
###############################################
def update(d,lam,L):
    line_1.set_ydata(intensity(y_array,d,lam,L))    
    fig.canvas.draw_idle()
    return


#Define control elements
###############################################
###############################################
s1=widgets.FloatSlider(
    min=0.,
    max=100.,
    step=1.,
    value=10.,
    layout=Layout(width='500px'),
    description='$D\,[\mathrm{\mu m}]$',
    style = {'description_width': 'initial'})

s2=widgets.FloatSlider(
    min=100.,
    max=1000.,
    step=10,
    value=500,
    layout=Layout(width='500px'),
    description='$\lambda\,[\mathrm{nm}]$',
    style = {'description_width': 'initial'})

s3=widgets.FloatSlider(
    min=0.5,
    max=2.,
    step=0.01,
    value=0.5,
    layout=Layout(width='500px'),
    description='$L\,[\mathrm{m}]$',
    style = {'description_width': 'initial'})


#Connect controls to plot
###############################################
###############################################
out = interactive_output(update, {'d': s1, 'lam': s2, 'L': s3})


#Set layout
###############################################
###############################################
Vbox_layout = Layout(display='flex', flex_flow='column', justify_content='space-between', align_items='center')


#Display output
###############################################
###############################################
display(VBox([s1, s2, s3], layout=Vbox_layout))

VBox(children=(FloatSlider(value=10.0, description='$D\\,[\\mathrm{\\mu m}]$', layout=Layout(width='500px'), s…

About the Visualization

Plot: The time-averaged intensity of light of wavelength $\lambda$ transmitted through a single slit of width $D$, projected on a screen a distance $L$ away. The intensity is shown as a function of $y\,[\mathrm{mm}]$. The small angle approximation is used for the spatial window that is displayed.

Sliders:

$D\,[\mathrm{\mu m}]$: vary the width of the slits.
$\lambda\,[\mathrm{nm}]$: vary the wavelength of the light.
$L\,[\mathrm{m}]$: vary the distance of the screen.

Exploration

Consider the following questions and possible actions:

How does the intensity pattern depend on the parameters $D$, $\lambda$, and $L$?

Viewing the Code

You are encouraged to click the button below to view the source code. You can alter the code and rerun it within this notebook, or download the notebook itself and run the code locally on your own machine.

In [24]:

#The code in this block includes content from StackOverFlow User: harshil (CC BY-SA 4.0)
#and can be found here: https://stackoverflow.com/questions/27934885/how-to-hide-code-from-cells-in-ipython-notebook-visualized-with-nbviewer
###############################################
###############################################
#Enable hidden code
from IPython.display import HTML

HTML('''<script>
code_show=true; 
function code_toggle() {
 if (code_show){
 $('div.input').hide();
 } else {
 $('div.input').show();
 }
 code_show = !code_show
} 
$( document ).ready(code_toggle);
</script>
<form action="javascript:code_toggle()"><input type="submit" value="Click here to toggle on/off the raw code."></form>''')

Out[24]: