This well-observed phenomenon has, besides several others, always been a fascination to me. We are well aware of several theories, experiments, and practical applications of this well-known phenomenon, but is it established what goes on at the grassroots of reflection?
My high school teacher once told me that whenever light is incident on any reflecting surface, its electrons absorb the energy of the photon and release back the same energy. If this is actually true, then I have plenty of questions to continue, but if it is not, then what is reflection, and how and why does it take place?
Answer
The question What IS reflection? is really a duplicate of yours, but I suspect the answer may be a bit brief for you.
A light wave, like any electromagnetic wave, is a combination of an oscillating electric and magnetic field. These fields exert an oscillating force on the electrons in any material the wave hits, and those electrons start oscillating in response. However an oscillating electron emits electromagnetic radiation, and this radiation interferes with the incident light.
To calculate what happens at the interface, you have to take into account the incident light, the light reradiated away from the solid back into the vacuum, (i.e., the reflected light) and the light reradiated into the body of the solid, (i.e., the transmitted light). When you do this, you find light is reflected at the angle of incidence, and the light is transmitted at an angle given by Snell's law. The calculation is a bit messy, but if you are interested, lots of examples are yours for the cost of a quick Google.
Response to comment:
The oscillations of the electrons are driven by the incoming EM field, so the oscillation frequency is the same as the frequency of the incoming light. The phase need not be (which is the origin of the refractive index change).
In the real world, the reflection is not independent of colour (i.e., the frequency of the light), and this phenomenon is known as dispersion. It is also not independent of light intensity, which is known as non-linearity, though non-linearity is usually an extremely small effect.
The electrons do not react instantly when the light strikes. The fastest frequency at which they can react is the plasma frequency.
Response to response to comment:
Energy can be lost due to interactions with the lattice, and indeed this is the norm, so the sum of the reflected and transmitted waves is generally less than the incident wave. The lost energy ends up as heat i.e., lattice vibrations.
However the fact energy is lost does not change the frequency of oscillation of the electrons, because that is determined by the incident light. That means the frequency of the reflected and transmitted light is the same as the incident light i.e., the same colour.
If the incident light contains different frequencies, like white light, then the result can be a shift in the perceived colour. For example, if you shine white light onto gold, the reflected light is yellowish. However the process of reflection is not changing the frequency of the light, but rather it is changing the relative intensities of frequencies in the reflected light by absorbing some frequencies more strongly than others.
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