The speed of light varies depending on the medium it passes through due to differences in the optical density of those materials. The general relationship between the speed of light in a vacuum (\(c\)) and the speed of light in another medium (\(v\)) is described by the refractive index (\(n\)) of that medium. The refractive index is defined as:
\[ n = \frac{c}{v} \]
From this equation, we can determine the speed of light in various mediums:
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Vacuum: In a vacuum, the speed of light is approximately \(c = 3.00 \times 10^8\) meters per second. The refractive index is 1 because there is no medium to slow light down.
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Air: The speed of light in air is very close to that in a vacuum, with a refractive index of about \(n \approx 1.0003\). Thus, the speed of light in air is slightly less than in vacuum, around \(v \approx 2.999 \times 10^8\) m/s.
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Water: The refractive index of water is approximately \(n \approx 1.33\). Therefore, the speed of light in water is:
\[ v \approx \frac{c}{1.33} \approx 2.26 \times 10^8 \text{ m/s} \]
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Glass: The refractive index of typical glass varies but is often around \(n \approx 1.5\). The speed of light in glass can be calculated as:
\[ v \approx \frac{c}{1.5} \approx 2.00 \times 10^8 \text{ m/s} \]
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Plastic: The refractive index of plastic can vary depending on the type, generally ranging from about \(n \approx 1.4\) to \(n \approx 1.6\). For example, if we take \(n \approx 1.5\), then the speed of light in plastic would be similar to that in glass, around \(v \approx 2.00 \times 10^8\) m/s.
In summary, the speed of light is fastest in a vacuum and decreases in denser mediums, such as water, glass, and plastic, due to their higher refractive indices. This change in speed also leads to effects such as refraction when light passes from one medium to another.