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When light passes through a medium, such as glass or water, its speed can be slower than its speed in a vacuum. This phenomenon is known as the slowing down or reduction of the speed of light in a medium. It occurs due to the interaction of light with the atoms or molecules in the medium.

To understand why light slows down in a medium, we need to consider the nature of light as an electromagnetic wave. Light consists of oscillating electric and magnetic fields that propagate through space. In a vacuum, these fields oscillate at a specific frequency and propagate at the speed of light, denoted by 'c,' which is approximately 299,792,458 meters per second.

When light enters a medium, the electric fields of the light wave interact with the charged particles (electrons and nuclei) in the atoms or molecules of the medium. These charged particles can be influenced by the electric field of the light wave and start to oscillate as well.

As the charged particles in the medium oscillate, they re-emit the light waves in different directions. This process effectively slows down the overall propagation of the light wave through the medium. The re-emitted waves from the oscillating charged particles interfere with the original wave, causing a delay in the overall propagation speed.

The delay arises because the oscillation of the charged particles takes time, and the energy from the original light wave is being momentarily absorbed and then re-emitted in different directions. This absorption and re-emission process results in a slower overall speed of light through the medium.

The interaction between light and matter in a medium can be further understood by considering the refractive index (n) of the medium. The refractive index is a dimensionless quantity that describes how much slower light propagates in a medium compared to its speed in a vacuum. It is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in the medium (v):

n = c/v

The refractive index determines the bending of light rays at the interface between two different media, a phenomenon known as refraction. The larger the refractive index of a medium, the slower the speed of light in that medium.

In summary, the slowing down of light in a medium occurs due to the interaction between the light wave and the charged particles in the atoms or molecules of the medium. This interaction leads to absorption and re-emission of the light, causing a delay in the overall propagation speed. The refractive index of the medium quantifies the degree of this slowing down.

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