Answer by Zhun-Yong Ong:
Metals are shiny because they have a lot of free (i.e. delocalized) electrons that form a cloud of highly mobile negatively charged electrons on and beneath the smooth metal surface in the ideal case. To simplify the discussion, we can think of these electrons as a negatively charged cloud in a uniform background of positive charge, forming a highly polarizable plasma.
A plasma is just a dense gas of charged particles and the distribution of the charges within its volume can be changed by applying an external electromagnetic (EM) field. In the absence of any external EM field, the charges in the plasma are uniformly distributed within the metal. So, there are no regions within the metal that are more negatively charged than the other.
Reflection of light
Light is nothing more than a propagating EM wave. An incoming or incident beam of light creates an oscillating EM wave on the surface of the metal and disturbs the plasma. The electron plasma on the metal surface then becomes polarized by the incoming light and starts to oscillate in phase with the electric field.
Let me explain what this means. The incident light creates an EM wave on the surface of the metal like in the picture below.
Thus, some areas on the surface of the metal become more positive while others are more negative. Because of this unevenness in the EM field on the surface, the electrons leave the negative regions (valley) and pile up in the more-positive regions (trough), like in the picture below. This create a rippling wave pattern in the spatial distribution of the electrons which were previously uniformly spread out. We call this wave pattern (or ripples in the plasma) resulting from the piling up of electrons in fixed places “polarization”. In short, the electron cloud is polarized.
One thing we have to bear in mind is that the wave-like motion of the incident EM wave means that the ripples in the plasma are moving in space and time. So, the free electron also have to move along with the incident EM wave and pile up at the right places to maintain that rippling motion. This act of following the incident electric field depends on the “mobility” of the electrons. In the ideal metal, the electrons can rush instantaneously to the positive spots and follow the EM wave with no lag. In this case, we say that the electrons form an infinitely polarizable plasma. By infinitely polarizable, we mean that the ripples in the plasma can be as big as they need to be stop the incident EM wave from penetrating the surface of the metal.
However, the oscillation of the electron plasma creates another electromagnetic (“polarization”) field that is out of phase with the incident EM wave (see green dashed lines in the above picture). In layman language, this means that the rippling in the plasma generates another EM field that opposes the original EM wave. It opposes rather than reinforces the original EM wave because the act of creating the ripples in the plasma uses up the energy from the original EM wave.
In the ideal metal, the EM wave generated from polarization cancels out 100 percent of the original incident EM wave inside the metal. In other words, the EM wave has been totally converted into ripples in the plasma. Thus, the incident light is stopped cold* and cannot penetrate into the bulk of the metal. Outside of the metal, the EM wave from the polarization is directed outwards away from the surface and constitutes the reflected light.
In the non-ideal case, the ripples in the plasma decay after a while. You can think of it as being caused by the electrons tiring out from trying to dancing in step with the incident EM wave. Hence, in order to sustain its oscillatory motion, it has to continually ‘steal’ a bit of energy from the incident light, and the light that is reflected from the surface is at a lower intensity than the incident light.
Metals are also crystals i.e. they form a perfectly ordered repeating geometrical structure. Therefore, its surface is usually smooth. When light reflects off a smooth surface, it looks shiny. A rough surface has a diffused look because the phases of the incident light are somewhat randomly distributed which destroys the coherence of the reflected light.
explains this better. Please upvote his answer.
(*) Not really. There is something called the skin depth which measures how deep the light can penetrate beyond the surface and is a consequence of the fact that in real metals, electrons do not respond instantaneously to the motion of the incident EM wave. High-frequency EM waves like X-rays move far too quickly for the electrons to keep up. This is why we use X-rays for imaging.