The speed of light in vacuum is:
299,792.458 km/s
Understanding the Speed of Light in Vacuum
The speed of light in a vacuum is one of the fundamental constants of physics. It is denoted by the symbol \(c\). This speed is the maximum speed at which conventional matter, energy, or any signal carrying information can travel through space.
The Accepted Value of the Speed of Light
The speed of light in vacuum is precisely defined. Since 1983, the meter has been defined in terms of the speed of light. Specifically, one meter is the length of the path travelled by light in vacuum during a time interval of \(1/299,792,458\) of a second. This definition fixes the speed of light in vacuum at exactly \(299,792,458\) meters per second.
To express this value in kilometers per second, we need to convert meters to kilometers. Since \(1\) kilometer is equal to \(1000\) meters, we divide the value in meters per second by \(1000\):
\(c = 299,792,458 \text{ m/s}\)
\(c = \frac{299,792,458}{1000} \text{ km/s}\)
\(c = 299,792.458 \text{ km/s}\)
Analyzing the Given Options
Let's compare the calculated value of the speed of light in vacuum with the options provided:
- Option 1: \(499,792.458 \text{ km/s}\)
- Option 2: \(299,792.458 \text{ km/s}\)
- Option 3: \(199,792.458 \text{ km/s}\)
- Option 4: \(399,792.458 \text{ km/s}\)
Comparing the calculated value \(299,792.458 \text{ km/s}\) with the options, we see that Option 2 matches the precise value of the speed of light in vacuum expressed in kilometers per second.
Identifying the Correct Speed of Light Value
Based on the internationally accepted definition and the conversion to kilometers per second, the speed of light in vacuum is \(299,792.458 \text{ km/s}\). This value is exact by definition of the meter.
| Option | Value (km/s) | Comparison |
|---|---|---|
| 1 | \(499,792.458\) | Incorrect |
| 2 | \(299,792.458\) | Correct |
| 3 | \(199,792.458\) | Incorrect |
| 4 | \(399,792.458\) | Incorrect |
Thus, the correct speed of light in vacuum among the given options is \(299,792.458 \text{ km/s}\).
Revision Table: Key Concepts
| Concept | Description |
|---|---|
| Symbol for Speed of Light | \(c\) |
| Medium for Speed \(c\) | Vacuum |
| Value in m/s | \(299,792,458\) m/s (exact) |
| Value in km/s | \(299,792.458\) km/s (exact) |
| Nature of \(c\) | Fundamental physical constant |
Additional Information on Speed of Light
The speed of light is not constant when it travels through a medium other than a vacuum, such as air, water, or glass. In these media, light travels slower than \(c\). The ratio of the speed of light in vacuum \(c\) to the speed of light in the medium \(v\) is called the refractive index \(n\) of the medium:
\(n = \frac{c}{v}\)
Since \(v < c\) in any medium, the refractive index \(n\) is always greater than 1 for media other than vacuum. For vacuum, \(v = c\), so \(n = 1\).
The speed of light in vacuum is also the speed at which all massless particles and field perturbations, including electromagnetic radiation such as light, propagate in a vacuum.
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