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I came across a question related to the multiple image formation from a thick mirror due to partial refraction and reflection. It was asked that which image would be the most intense? In the solution second image was given as the most intense with the reasoning that the percentage of rays getting refracted would be more than that of reflected rays. Although I understood the solution but I couldn't understand the exact reason behind this statement. Could someone please throw some light on this topic?

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  • $\begingroup$ More rays refracted than rays reflected sounds like a necessary property of transparent material don't you think? $\endgroup$
    – Naptzer
    Nov 15, 2021 at 7:40
  • $\begingroup$ Yes, you're absolutely correct but I was wondering what exactly makes this happen? $\endgroup$
    – Aspirant
    Nov 15, 2021 at 8:28

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Reflection and refraction of light rays through a medium are related to the medium´s physical properties and the angle formed with the normal direction with respect to the object´s surface.

The most important property in this problem is the refractive index "n": $$n=\frac{c}{v}$$ where "c" is the light´s speed in vacuum and "v" is the light´s speed in the medium. This link to wikipedia can explain you a lot more about the microscopic reason for the change of light´s speed: https://en.wikipedia.org/wiki/Refractive_index

In this wikipedia page, the subsections "refraction", "total internal reflection", and "reflectivity" are very elucidative. You will see that "transparent mediums" have a higher refractive index, and because of that there are more angles that makes the refraction possible than total reflection possible.

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At an interface between two transparent media, the fractions of power that are transmitted (i.e. refracted) and reflected are governed by the Fresnel equations, which provide the explicit dependence of the reflectance and the transmittance at the interface in terms of

  • the relative refractive indices of the two media,
  • the angle of incidence, and
  • the polarization of the light beam.

For most angles of incidence, and for reasonable combinations of media, the transmittance is higher than the reflectance. However, for high angles of incidence (close to 90° or to the critical angle, whichever is lower) the trend reverses, and "more rays" get reflected than refracted (flawed as that language is).

I appreciate that this isn't really answering the core question of why this happens, but I suspect there isn't a single, clear, simple explanation for this. The Fresnel equations embody the Maxwell equations of electrodynamics when they are applied to the bound charge and current distributions that are induced at the interface as a result of the differing polarizabilities of the two media. It might be possible to look at that analysis and provide a physics-based response there, but I've never seen it done $-$ but, in any case, if you want that answer, you need to start with an in-depth understanding of the derivation of the Fresnel equations and the physics involved there.

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