100 Nano-Stories: Photons!

Episode #79: Photons In Optics Introduction!

Carlos Manuel Jarquín Sánchez
5 min readApr 23, 2021

Preface! ✨

It’s your favorite material science & nanotechnology enthusiast! Today, I will cover more about the photon in an abstract way/explanation.

I made the mistake of explaining Mie Scattering without explaining the Photon in its entirety, so I want to make things clearer for you if you are confused about the article.

If you don’t know what I’m talking about, you can read it, but I highly suggest reading this article before you go diving into Mie Scattering.

In a nutshell, the article above talks about:

  • The Incident Wavelength of Light and the particle size can play a huge role if the scattering will obey Rayleigh Scattering or Mie Scattering.
  • Instead of using the extinction coefficient to find out the scattering efficiency of the particles, we used The Scattering Cross-Section which is where the radiation–target interaction occurs (radiation is the wavelength of light, the target is the particle).
  • The Geometry of Mie Scattering says that once we reach a particle size of 2π or 1 (which is a constant number), we begin to oscillate and the frequency of the wavelengths get smaller and smaller, which pushes more towards blue, violet, and Ultraviolet (UV) Wavelengths of light, which is backed by The Optical Theory.

But let’s get to the main point of what a photon is! By the time you finished this article, you’ll be surprised by how fast it took to explain a photon! 😉

Photons Explained! 💡

Concept + Definitions! 🔑

A photon is a massless object/particle that travels at the speed of light (299, 792, 458 meters/second).

A photon can carry momentum (despite it having no mass) because it can hit something like a proton/electron and give the proton/electron give momentum. Momentum is the movement of something, and it is calculated by multiplying the mass of the object moving times the object’s velocity.

Finally, the energy in an individual photon is a specific number, which means it can’t go over or under this number (the photon energy is quantized). The formula for calculating the energy of a photon is this:

E =h(c)/λ

E → Energy Of A Photon.

h → Planck’s Constant (6.62607015×10^-34 Joules (J) times seconds (s)).

c → Speed Of Light (299, 792, 458 meters (m)/second (s)).

λ → Wavelength (of a certain light like Visible, UV, etc.).

Rayleigh Scattering Problem! 🔑

Let’s apply the energy equation to find out how many joules (energy) a typical wavelength of blue light contains! The wavelength of blue light is between 450–500 nanometers.

In this case, let’s focus more on the shorter wavelengths of blue light, so let's use 450 nanometers!

E =h(c)/λ with the numbers applied to the equation looks like this:

E = (6.62607015 × 10^-34 J*s)(299, 792, 458 m/s) / 450 × 10^-9 meters (aka 450 nanometers)

If we throw all of those numbers into a calculator, we end up with about 4.41733 10^-19 Joules.

That is such a small number, but this is one photon with the same wavelength as blue light. Now imagine all the wavelengths of blue light being scattered in the sky! 😵

But because the number 4.41733 10^-19 Joules is such a small number, physicists and scientists prefer to use something called Electron Volts (eV).

To change the conversion from Joules to electron volts, we multiply our old number times 1 eV/ 1.6 × 10^-19 Joules. The reason we use this number is that 1.6 × 10^-19 Joules is the same as 1 Coulomb (SI Unit of electric charge) since photons are electromagnetic waves and carry charge & radiation with them.

So we can use the equation like this to convert from Joules to eV:

4.41733 10^-19 Joules × 1 eV/ 1.6 × 10^-19 Joules.

All you have to do is divide 4.41733/1.6 to covert to eV since both sides of Joules contain the same power of 10^-19.

4.41733/1.6 ≈ 2.76 eV.

This means that the shortest wavelengths of blue light have the usual energy of approximately 2.75 or 2.76 eV.

Closing Thoughts! 💭

Now that I have introduced the photon in an abstract form, I can slowly go more into the mathematics behind Rayleigh Scattering and how we end up with an intensity that is inversely proportional to 1/λ⁴! ✌🏽

If I didn’t clarify well enough in this article, please throw a comment, and I will edit this to help you understand more about Photons, Rayleigh, and Mie Scattering!

Vocabulary! 📓

E → Energy Of A Photon.

h → Planck’s Constant (6.62607015×10^-34 Joules (J) times seconds (s)).

c → Speed Of Light (299, 792, 458 meters (m)/second (s)).

λ → Wavelength (of a certain light like Visible, UV, etc.).

Momentum → The movement of something, and is calculated by multiplying the mass of the object moving times the object’s velocity.

Coulomb → International System (SI) Unit of Charge

Joules → Derived Unit to measure Energy (derived from International System)

Amplitude → The amplitude starts at the middle/origin to the crest/hilltop of a wave.

Wavelength The distance between two tops (crests) of an electromagnetic wave.

Rayleigh Scattering → The wavelength of a certain ray of light is short, then the wavelength of light will scatter more than a ray of light where the wavelength is larger, and Rayleigh Scattering tends to scatter blue light because of its wavelength (450–485 nanometers).

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).

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