Velocity of Light in Different Mediums

The speed at which light travels depends on the medium through which it is passing. Light travels fastest in a vacuum. When light enters any material medium, its speed decreases.

Factors Affecting Velocity of Light

The velocity of light in a medium is related to the optical density of the medium, which is often quantified by its refractive index. The relationship between the speed of light in vacuum (\(c\)), the speed of light in a medium (\(v\)), and the refractive index of the medium (\(n\)) is given by:

\(v = \frac{c}{n}\)

From this formula, we can see that:

• The speed of light (\(v\)) is inversely proportional to the refractive index (\(n\)).
• A lower refractive index means a higher speed of light.
• A higher refractive index means a lower speed of light.

Comparing Velocity of Light in Given Mediums

Let's look at the approximate refractive indices for the given mediums:

• Vacuum: \(n_{vacuum} \approx 1.000\)
• Air: \(n_{air} \approx 1.0003\)
• Water: \(n_{water} \approx 1.33\)
• Glass: \(n_{glass} \approx 1.5 \text{ to } 1.7\) (depends on the type of glass)

Since the speed of light is \(v = c/n\), the medium with the lowest refractive index will have the maximum velocity of light.

Comparing the refractive indices:

\(n_{vacuum} < n_{air} < n_{water} < n_{glass}\)

Therefore, the speeds of light in these media will be:

\(v_{vacuum} > v_{air} > v_{water} > v_{glass}\)

The speed of light in vacuum is the maximum possible speed of light, often denoted as \(c \approx 299,792,458\) meters per second.

Conclusion

Based on the relationship between the speed of light and the refractive index, light travels fastest in the medium with the lowest refractive index. Among the given options, vacuum has the lowest refractive index (approximately 1). Air has a refractive index very close to that of vacuum, but slightly higher. Water and glass have significantly higher refractive indices compared to vacuum and air.

Thus, the velocity of light is maximum in Vacuum.