Skip to content

Instantly share code, notes, and snippets.

@jmoy
Last active November 18, 2018 19:51
Show Gist options
  • Save jmoy/4dda9b8b8e2b3eb27666bd6ebe208ea3 to your computer and use it in GitHub Desktop.
Save jmoy/4dda9b8b8e2b3eb27666bd6ebe208ea3 to your computer and use it in GitHub Desktop.
Why soap bubbles are colorful and windowpanes are not
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Why soap bubbles are colourful and windowpanes are not"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Last night I was blowing soap bubbles for my two and a half year old daughter, and she was fascinated by them. \"Colours! Colours!\" she would exclaim.\n",
"\n",
"In school we learnt that soap bubbles are colourful because of the wave nature of light. The light reflected from the front surface of the bubble [interferes](https://en.wikipedia.org/wiki/Thin-film_interference) with the light reflected by the back surface. For colors where the waves are in the same phase the amplitudes add up and we get a strong reflection. For colors where the waves are in opposite phase they cancel each other out and we get no reflection. \n",
"\n",
"Being a somewhat dumb student in school it never occured to me to ask why this happens with only thin films like soap bubbles or an oil film on a wet road but not when the two reflecting surfaces are far apart like in a windowpane. After all, the intereference effect depends on the phase difference between the two reflections, which in turn depends on the remainder from dividing the distance between the two reflecting surfaces by the wavelength of the incident light, i.e. if the wavelength is $\\lambda$ and the distance between the surfaces is $d$ then the phase difference between the reflections from the two surfaces would be\n",
"\n",
"$$\\phi(\\lambda)=4\\pi\\left({d \\over \\lambda} - \\left\\lfloor{d \\over \\lambda}\\right\\rfloor \\right)$$\n",
"\n",
"and $\\phi(\\lambda)$ would change with $\\lambda$ even when $d$ is large as in a windowpane.\n",
"\n",
"So why isn't the reflection from windowpanes colourful like reflections from soap bubbles? Googling about it a bit leads to many answers which rely on the lack of [coherence](https://en.wikipedia.org/wiki/Coherence_%28physics%29) in the light source. But coherence is not really the answer. At least not directly.\n",
"\n",
"Any wave, whether coherent or not, can be broken up using Fourier analysis into a sum of monochromatic components. We can apply the intereference logic to each monochromatic component and still get constructive and destructive inference.\n",
"\n",
"The answer lies really in arithmetic. In the formula above for a given range of $\\lambda$, say the visible spectrum, when $d$ is small relative to the typical lambda, $\\phi(\\lambda)$ has typically few peaks and troughs and so in the net reflection after interference some colours dominate while others are absent. Whereas for large $d$, the peaks and troughs of $\\phi(\\lambda)$ occur many times in a given range of $\\lambda$ and therefore in the net reflection after interference we have the same color distribution as in the incident light.\n",
"\n",
"Only after understanding this can we make a connection to coherence. A supposedly monochromatic light source is never exactly monochromatic, there is some spread of wavelength. The sharper the concentration of wavelengths, i.e. the more coherent the source, the less chance that many peaks and troughs of $\\phi(\\lambda)$ will fit into the wavelength range present and destroy the interference.\n",
"\n",
"Below I illustrate this by plotting $\\phi(\\lambda)$ for different values of $d$. All distances are in nanometers."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The definition of $\\phi(\\lambda)$"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def plot_phi(d,N=100):\n",
" #Visible spectrum from violet to red\n",
" lambdas = np.linspace(400,600,N)\n",
" #(Half of) Phase difference in waves reflected from front and back\n",
" phdiff = 4*np.pi*(np.fmod(d,lambdas)/lambdas)\n",
" # The strength of the net wave after interference\n",
" strength = np.abs(np.cos(phdiff/2))*2\n",
" plt.plot(lambdas,strength,\".\")\n",
" plt.xlabel(\"Wavelength (nm)\")\n",
" plt.ylabel(\"Strength of reflection\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Soap bubbles"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A 700nm soap bubble reflects strongly in blues,"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f44b5d285c0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_phi(700)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"whereas a 750nm bubble reflects strongly in the green."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f44ad7dc4e0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_phi(750)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Of course in a actual soap bubble the thickness varies from place to place and so we see a variation of colors."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Windowpane"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Consider now a 5mm windowpane. We plot with a frequency grid with a large number of points to bring out the pattern well."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f44ad6b0080>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(20,4))\n",
"plot_phi(5e6,2000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There are strong reflections from all parts of the spectrum so for ordinary light we would see a reflection of the same color as the incident beam."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
@popey456963
Copy link

A thrilling story @r3plicon, however, I'm not sure that entirely relates to the post. If the soap is in your mouth, I imagine it's fairly hard to see light interefence and the colours it produces.

@Iteratix
Copy link

I think @r3plicon seems to be some kind of bot? https://github.com/r3plicon/IC-class-

@TheAnig
Copy link

TheAnig commented May 12, 2018

This is a very interesting read. More interesting is the fact that you demonstrated by calculation what students would normally have to convince themselves by trying out one or two points. This is a very interesting approach. Kudos to you man!

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment