Explanation:

Electromagnetic waves are waves that consist of oscillating electric and magnetic fields. They are transverse waves, which means that the electric and magnetic fields are perpendicular to the direction of wave propagation. Electromagnetic waves can propagate through a vacuum as well as through a medium.

When an electromagnetic wave propagates through a medium, such as a dielectric, its speed changes. The speed of an electromagnetic wave in a dielectric is slower than its speed in a vacuum. This can be explained by the fact that the electric field of an electromagnetic wave induces a polarization in the dielectric, which in turn generates an electric field that opposes the original electric field. This opposing electric field slows down the wave.

Formula:

The speed of an electromagnetic wave in a dielectric can be calculated using the following formula:

v = c/n

where v is the speed of the wave in the dielectric, c is the speed of light in a vacuum, and n is the refractive index of the dielectric.

Examples:

- The speed of light in a vacuum is approximately 3 x 10^8 m/s. The speed of light in water is approximately 2.25 x 10^8 m/s, which is slower than its speed in a vacuum.
- The refractive index of a material is a measure of how much the speed of light is reduced when it passes through that material. The refractive index of water is approximately 1.33, which means that the speed of light in water is approximately 1/1.33 = 0.75 times its speed in a vacuum.

Conclusion:

In conclusion, electromagnetic waves propagate slower in a dielectric than in a vacuum. This is due to the polarization of the dielectric, which generates an electric field that opposes the original electric field of the wave. The speed of an electromagnetic wave in a dielectric can be calculated using the formula v = c/n, where v is the speed of the wave in the dielectric, c is the speed of light in a vacuum, and n is the refractive index of the dielectric.