Why light reflects off a surface? And what causes the phenomena of the total internal reflection? I have just watched two videos on the YouTube channel "Fermilab" about why light slows down in transparent mediums and why light refracts when moving between transparent mediums.
These two videos made me curious about light reflection off surfaces. I would like to know the exact mechanism.


*

*What happens down at the atomic level when a ray of light is incident on a surface?

*What causes light to reflect at the same angle as the incident light?

*And in certain cases, why total internal reflection happens?

 A: This is a QM answer. You are asking about reflection, so I am going to talk about the visible wavelength photons.
When a photon interacts with an atom, three things can happen:


*

*elastic scattering, the photon keeps its energy and phase and changes angle

*inelastic scattering, the photon keeps part of its energy and phase and changes angle

*absorption, the photon gives all its energy to the absorbing atom
Now you are asking about reflection, that is 1. elastic scattering. When light shines on an object, and we see it (the object) is because all three happen, it is just the ratio of these that is different. For reflection, most of the photons get elastically scattered, and a lower ratio of photons get inelastically scattered, and absorbed.
There are two basic types of reflection:


*

*specular (mirror like), in this case, most of the photons get elastically scattered, and keep their relative angle and phase, and energy levels. This is the only way to build a mirror image (like shiny metals, or glass reflection).

*diffuse (non-mirror like), in this case, the photons relative angle is not kept, the incident photon's angle does not decide the reflected photons' angle. The reflected photons' angle is random (like a wall).
You are asking what makes the reflected photons' angle the same as the incident photons'. Now this is only true In the case of specular (mirror-like reflection). The reason for this is the lattice structure of the medium. When the photons interact with the lattice structure's atoms, the incident photons' partial waves interfere. 
Now this interference can be:


*

*constructive, in only one single angle, that is the same as the incident angle

*destructive, in all other angles
The incident photons', as per QM travel all paths through space, but their partial waves create desctructive interference in all other directions, except for the one that is the same as the incident angle, that is where the partial waves create constructive interference, and the reflected photon's angle will be that one.
It is very important to understand that you are asking about reflection, and not just why we see objects.
The reason why we see objects is:


*

*reflection (elastic scattering)

*absorption, and re-emission
All objects we see, emit/reflect photons, that is how we see them. Now the ratio of these two is different with different materials.
With shiny metals (or glasses), the ratio of reflection (elastic scattering) is dominant. That is why we say that metals do not have their own color (except gold), because they reflect most visible light. These materials do absorb some of the photons too, just the ratio of these is very little.
Other materials, like a wall, absorb a lot of photons, and re-emit them at a certain energy level, depending on the surface (lattice structure emission spectrum). This surface does reflect (elastically scatter) some photons too, but their ratio is very little. This is why a wall (and other non shiny materials) do have their own colors.
You are asking why total internal reflection happens.


Total internal reflection (TIR) is the phenomenon that makes the water-to-air surface in a fish-tank look like a perfectly silvered mirror when viewed from below the water level (Fig. 1). Technically, TIR is the total reflection of a wave incident at a sufficiently oblique angle on the interface between two media, of which the second ("external") medium is transparent to such waves but has a higher wave velocity than the first ("internal") medium.


https://en.wikipedia.org/wiki/Total_internal_reflection
What this means is that when you are inside the water, and there is air above the water level, the photons inside the water, that try to escape the water into the air, get reflected (most of the photons get elastically scattered). Some photons do get refracted (travel into the air), and some get inelastically scattered, and some get absorbed, but the ratio of these is very little.
The boundary between the water (when looking from inside the water) and the air acts like a mirror:


*

*it causes specular reflection, the relative phase, angle, and energy level of the photons is kept

*most of the photons get elastically scattered
This is the only way to create a mirror like image when looked from inside the water.
