How to set an appropriate point of view?

Question

How to set xlim and ylim to see both cureves (omega and y) on a plot? Or how to verify that it is not possible?

import matplotlib.pyplot as plt
import numpy as np

e = 1.602176634e-19
m_e = 9.1093837015e-31
k = np.arange(0.00001, 50000, 0.003)
eps_0 = 8.8541878128e-12
n_0 = 100
c = 299792458
omega_p = np.sqrt(n_0*e**2/(eps_0*m_e))           
omega = np.sqrt(omega_p**2+c**2+k**2)

y = k*c

fig, ax = plt.subplots()
plt.rcParams["figure.figsize"] = [5, 5]

# Plot
ax.yaxis.set_label_coords(-0.07, 0.84)
ax.xaxis.set_label_coords(0.95, -0.05)
ax.set_xlabel(r'$k$')
ax.set_ylabel(r'$\omega$', rotation='horizontal')
ax.set_xlim(10000, 40000)
ax.set_ylim(299792454, 299792462.1700816)
ax.plot(k, omega)
ax.plot(k, y)

# Focusing on appropriate part
print(omega[1000000]-omega[999999])
print(omega[-1]-omega[-2])
print(len(omega))
print(k[1000000])
print(k[-1])
print(omega[1000000])
print(omega[-1])
print(y[int(ax.get_xlim()[0])])
print(y[int(ax.get_xlim()[1])])
plt.show()

The output now:

There should be also an assymptote.

Answer 1

An idea is to just let matplotlib choose its default limits. Then you can interactively zoom in to an area of interest. The code below sets a log scale for the y-axis, which might help to fit everything. In order to avoid too many points, the 16 million points of np.arange(0.00001, 50000, 0.003) are replaced by np.linspace(0.00001, 50000, 10000).

import matplotlib.pyplot as plt
import numpy as np

e = 1.602176634e-19
m_e = 9.1093837015e-31
# k = np.arange(0.00001, 50000, 0.003)
k = np.linspace(0.00001, 50000, 10000)
eps_0 = 8.8541878128e-12
n_0 = 100
c = 299792458
omega_p = np.sqrt(n_0 * e ** 2 / (eps_0 * m_e))
omega = np.sqrt(omega_p ** 2 + c ** 2 + k ** 2)

y = k * c

fig, ax = plt.subplots()
plt.rcParams["figure.figsize"] = [5, 5]

ax.set_xlabel(r'$k$')
ax.set_ylabel(r'$\omega$', rotation='horizontal')
ax.plot(k, omega, color='blue')
ax.plot(k, y, color='red')
ax.set_yscale('log')
plt.show()