100 Nano-Stories: Is Beer’s Laws Breakable (Part 3)?

Episode #76: Mie Scattering + Mie Theory Introduction!

Carlos Manuel Jarquín Sánchez
4 min readApr 19, 2021

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Preface! ✨

It’s your favorite material science & nanotechnology enthusiast! Today, we will cover a new theory and form of scattering that can be used to calculate absorption and scattering coefficients in transparent aerogels!

If you need a reminder of the Beer-Lambert Law Violations, I highly recommend you read this article!

TL;DR → Beer’s Law Violations (Part 2)! 🔑

These main laws are the ones that could be violated and render Beer’s Law “unusable” to calculate certain numbers like absorption & scattering coefficient:

  • The incoming wavelengths of light that enter the aerogel are not one wavelength of light only (monochromatic).
  • All the light that enters the aerogel should be in a parallel beam/parallel rays, to minimize the amount of scattering that could happen when the light is trying to directly transmit through the aerogel.
  • The absorbing particles inside the aerogel are distributed evenly throughout the aerogel without bumps or fancy shapes!

So, once the Beer-Lambert Law doesn’t work to calculate transmissivity because one of these laws is broken, what theory/equation can we look to for help? 🤷🏽‍♂️

Mie Scattering Explained! 💡

Concepts! 🔑

Mie Scattering is the scattering of an electromagnetic wave (light is an electromagnetic wave) by spherical particles in the air. Mie Scattering can occur with a spherical particle that either has the same diameter or larger than a certain wavelength of light that will enter the molecule/spherical particle (aka incident light).

For those wondering what is the diameter of a sphere, it is essentially drawing a line from one end of the sphere to the other end of the sphere, as long as the line passes through the center of the sphere.

D = Diameter.

But Why Mie Scattering? 🔑

If we go back to the Beer-Lambert Law, there is one “law” that happens in the aerogel that can hinder us from finding the scattering and absorption coefficients in the transparent aerogels.

This is the law:

  • The incoming wavelengths of light that enter the aerogel are not one wavelength of light only (monochromatic).

When light passes through a transparent aerogel, there is more than one wavelength of light passing through. There is the wavelength of light in the visible light spectrum (ROY G BIV), the wavelengths of light in the ultraviolet light spectrum (UVA, UVB, UVC), the infrared wavelengths of light, radio waves, etc.

This means that there is more than one type of wavelength of light passing through the aerogel is not monochromatic, and it breaks Beer’s Law! This is when we have to use Mie Scattering! 💥

Closing Thoughts! 💭

Now we understand why The Beer-Lambert Law is useful for certain applications, but this time, we gave a direct example of how it can be destroyed!

See you tomorrow for the “Mie Scattering Encyclopedia!” ✌🏽

The Beer-Lambert Law A relation of the logarithmic dependence of loss of radiant energy/intensity through a medium/material and the properties of the material the light is passing through.

Transmission CoefficientA measure of how much light can pass through a material (in this case, aerogel!) by calculating via the intensity of the wavelength of the light.

Mie Scattering → A form of scattering that can occur in a spherical particle that either has the same diameter or larger than a certain wavelength of light that will enter the molecule/spherical particle (aka incident light).

TransmissivityThe overall light that passes/diffuses through a medium/material.

Monochromatic → Contains only one wavelength of light and/or one color.

Incident Light → The light that will enter the molecule/spherical particle/material.

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© 2021 by Carlos Manuel Jarquin Sanchez. All Rights Reserved.

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