$$T = \frac{1}{1+F\sin^2(\delta/2)}$$ $$ F = \frac{4R}{(1-R)^2}$$ $$\delta = \frac{2\pi}{\lambda}2nl\cos\theta$$ is the phase difference between successive transmitted pair

In [1]: 
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
from ipywidgets import StaticInteract, RangeWidget
In [10]: 
x = np.linspace(-4*np.pi,4*np.pi,501)
def plot(r):
    fig, ax = plt.subplots(figsize=(5, 5),
                           subplot_kw={'axisbg':'#EEEEEE',
                                       'axisbelow':True})
    ax.grid(color='w', linewidth=2, linestyle='solid')
    F = 4*r/(1-r)**2
    ax.plot(x,1/(1+F*np.sin(x/2)**2), lw=5, alpha=0.4)
    #ax.set_xlim(-50, 50)
    ax.set_title('plot of transmittance vs phase and reflectance')
    ax.set_xlabel('delta')
    ax.set_ylabel('transmittance')
    ax.set_ylim(0, 1)
    return fig
In [11]: 
StaticInteract(plot,r=RangeWidget(0.0, 1.0, 0.1))
Out[11]:
r:

to-do

  • need to convert xticks to show delta/phase
In []: