Light's Refractive Index & Phase Change: Explained

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When light strikes a material with a certain thickness and refractive index, it experiences partial transmission and reflection. The transmitted light undergoes a consistent phase change of π upon exiting the material, regardless of thickness. This phase change is attributed to the properties of the medium and the boundary conditions at the interface. The discussion clarifies that the phase shift can only be π or zero, depending on the refractive indices on either side of the surface, and cannot be π/2 or 2π. Understanding these principles is crucial for applications in optics and material science.
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Consider a plane beam of light is falling normally on a material with thickness (d) and refractive index (n), the light partially transmits and partially reflects the light, so the light transmitting the light travels a distance (2nd) coming out of the material have a phase change of ∏ always, How? will it be different for different thickness?
If no why the phase change can't be ∏/2 or 2∏ or something else?
 
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There is usually a phase change associated with reflection - either zero or pi, depending on the refractive index either side of the surface.

The phase shift for light traversing a medium depends on the thickness of the medium and the refractive index.
 
I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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