DEMO: Black Body radiation#
import numpy as np
import matplotlib.pyplot as plt
from ipywidgets import interactive
from scipy.constants import h, c, k, e, N_A
%matplotlib inline
%config InlineBackend.figure_format='retina'
# Lets pick some beautiful colors
from matplotlib import cm
from cycler import cycler
magma = cm.get_cmap('magma', 10) # 10 discrete colors, feel free to change
plt.rcParams['axes.prop_cycle'] = cycler(color=[magma(i) for i in range(magma.N)])
/tmp/ipykernel_1782/4124089407.py:12: MatplotlibDeprecationWarning: The get_cmap function was deprecated in Matplotlib 3.7 and will be removed two minor releases later. Use ``matplotlib.colormaps[name]`` or ``matplotlib.colormaps.get_cmap(obj)`` instead.
magma = cm.get_cmap('magma', 10) # 10 discrete colors, feel free to change
def planck(wavelength, T):
"""
Planck's Law to calculate the spectral radiance of black body radiation at temperature T.
Parameters:
- wavelength (float): Wavelength in meters.
- T (float): Absolute temperature in Kelvin.
Returns:
- (float): Spectral radiance in W/(m^2*sr*m).
"""
exponent = (h*c) / (wavelength*k*T)
exponent = np.clip(exponent, None, 700) # Clip values of exponent at 700 to avoid numerical overflow
return (2.0*h*c**2) / (wavelength**5 * (np.exp(exponent) - 1))
def plot_black_body(T, show=False):
"""
Plot the black body radiation spectrum for a given temperature T.
"""
wavelengths = np.linspace(1e-9, 5e-6, 1000) # Wavelength range from 1 nm to 3 um
intensities = planck(wavelengths, T)
plt.plot(wavelengths*1e9, intensities, label=f'T={T}', lw=3) # Convert wavelength to nm for plotting
plt.xlabel('Wavelength (nm)')
plt.ylabel('$Intensity (W/m^2)$')
plt.grid(True)
plt.legend()
max_int = max(planck(wavelengths, 5000)) # lets limit y axis to 5000
plt.ylim(0, max_int)
if show: # show is needed for interactive plots
plt.show()
for T in range(3000, 5000, 200):
plot_black_body(T)
interactive(plot_black_body, T=(1000, 5000, 100), show=True)