# Preface! ✨

It’s your favorite material science & nanotechnology enthusiast! Today, I want to cover how the geometry of light can affect the scattering of light in a material or the sky! I will also cover some concepts in Rayleigh Scattering to explain the geometry of optics!

If you are confused about some of these concepts, I highly recommend reading this article to get up to speed on optical depth!

Don’t worry, it’s only a 5-minute read! 😁

Briefly, a summarization of the previous article:

• The optical depth is the quantity of light that has been removed due to absorption, scattering, and reflection.
• If the optical depth is greater than 1/e or 1, the medium/material will be opaque, and photons will either be absorbed, reflected, or scatter many times before transmitting/leaving the aerogel. This means you can’t really see what’s on the other side of the material, and it can cause a haze because of the absorption or scattering of the incoming light.
• If the optical depth is less than 1/e or 1, the medium/material will appear transparent, and photons will either transmit directly through the material without being absorbed or scattered.

But for now, let’s cover scattering, the geometry of scattering, and the applications towards Rayleigh Scattering in Transparent Aerogels!

# Scattering Explained! 💡

## Definitions + Concept! 🔑

Scattering (in terms of optics/light) is the change of direction of electromagnetic radiation/light from its original direction.

For some who may be asking about what absorption means from our absorption and scattering coefficients from previous episodes in “100 Nano-Stories”:

Absorption (in terms of optics/light) means that electromagnetic radiation is being converted into either heat or chemical energy because a medium/material absorbed the light.

If you didn’t know, you can see color because of light scattering. Certain colors are visible because of the size of the particles that the light passes through. For example, the sky is blue is because the particles and molecules in the air are about the same size as the wavelength of blue light, which is about 450–485 nanometers.

Optics is such a wonderful phenomenon! But let’s talk about how it works! 😉

## Optics Geometry! 🔑

When light hits a material/medium, there are many ways the light can scatter, but the effect the light does on the material will depend on the direction of the light once it’s scattered.

The first form of light is incident light. Incident light is the light that approaches you and hits you before it is scattered/reflected by a medium/material. Incident light travels in straight lines, whether horizontally or vertically.

An example is The Sun. The light that the Sun emits before it reaches you is the incident light.

The second form of light is scattered light. The scattered light is incident light that has been reflected at an angle. In other words, it has changed direction from its original direction before it got reflected by the medium/material.

Scattered light can travel in any direction. It can be transmitted through a material/particles (Direct Transmittance/Forward Scattering), scatter through the material/particles at an angle (Diffuse Transmittance), or reflect in the same direction the light came from (Diffuse Reflectance/Backscattering).

## Optical Depth, Single-Scattering Albedo, and Examples! 🔑

To calculate the scattering of light and the intensity of the light, we can use the single-scattering albedo!

The Single-Scattering Albedo is used to define the scattering and absorption in a medium/material.

The equation used to calculate the single-scattering albedo is:

ω = Single-Scattering Albedo symbol.

β(s) = The Scattering Coefficient.

β = The Extinction Coefficient.

The extinction coefficient (β(e)) is the sum of the absorption coefficient (β(a)) and the scattering coefficient (β(s)).

• If “ω” is 0, the medium/material will absorb everything (particles, photons, etc.).
• If “ω” is 1, the medium/material will scatter everything (particles, photons, etc.)

The darker (closer to the color black) something is, the single-scattering albedo (absorbance) will be closer to 0. One example is smoke.

The lighter (closer to the color white) something is, the single-scattering albedo (reflectance) will be closer to 1. One example is a cloud.

# Closing Thoughts! 💭

That was an interesting application towards Optical Depth, Scattering, and the Single-Scattering Albedo!

It also helps you have an understanding of why certain colors are reflected into our eyes and how the bending or change in direction of the light can affect the outcome of the material/medium that absorbed and/or reflected the light.

See you tomorrow for the Equations on Isotropics and Rayleigh Scattering! ✌🏽

# Vocabulary! 📓

Optical Depth → The quantity of light that has been removed due to absorption, scattering, and reflection; τ.

Scattering In terms of optics/light, it’s the change of direction of electromagnetic radiation/light from its original direction.

Incident LightThe light that approaches you and hits you before it is scattered/reflected by a medium/material. Incident light travels in straight lines, whether horizontally or vertically.

TransparencyAll the light will pass through a material, and it won’t be reflected, absorbed, or scatter in a material.

Absorption In terms of optics/light, it means that electromagnetic radiation is being converted into either heat or chemical energy because a medium/material absorbed the light.

Scattered LightIncident light that has been reflected at an angle. In other words, it has changed direction from its original direction before it got reflected by the medium/material.

The Extinction Coefficient → A sum of the absorption coefficient and the scattering coefficient; β(e).

Single-Scattering Albedo Defines the scattering and absorption in a medium/material.

Direct TransmittanceLight passes through the aerogel without scattering.

Diffuse TransmittanceLight passes through the aerogel and is scattered throughout the network of pores. The light will leave the aerogel at an angle rather than straight through the aerogel.

Diffuse ReflectanceLight enters through the aerogel and is reflected the way it entered through the aerogel due to scattering between the nano-sized particles.

Absorption Coefficient(β(a))

Scattering Coefficient(β(s))

Wavelength Symbol → λ