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Wave theory explains the propagation of light through a medium through the concept of electromagnetic waves. According to this theory, light is an electromagnetic wave composed of electric and magnetic fields oscillating perpendicular to each other and to the direction of propagation.

When light travels through a medium, such as air, water, or glass, it interacts with the atoms or molecules in that medium. These interactions cause the electromagnetic wave to slow down and change direction, a phenomenon known as refraction. The degree of refraction depends on the properties of the medium, such as its refractive index.

The refractive index of a medium is a measure of how much the speed of light is reduced when it enters that medium compared to its speed in a vacuum. It is typically denoted by the symbol "n." When light passes from one medium to another with a different refractive index, the change in speed causes the wavefronts to bend, resulting in the change in direction.

The wave theory of light successfully explains various phenomena observed in the propagation of light, such as diffraction and interference. These phenomena arise due to the wave nature of light and the interaction of light waves with each other or with obstacles in their path.

It is worth noting that the wave theory of light is an approximation that works well for many situations, but in certain cases, such as when dealing with very small scales or low intensities, the particle nature of light (photons) becomes more prominent, and quantum mechanics provides a more accurate description.

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