The speed of light is the speed at which light — and every other electromagnetic wave — travels through empty space (vacuum). It is one of the most important constants in physics, denoted c:
c≈3×108m/s=3×105km/s
More precisely c=2.998×108m/s. In one second light travels about 300,000 km — roughly seven and a half times around the Earth.
Where the Value Comes From (Maxwell)
The speed of light is not just measured; it is predicted by Maxwell's equations. When Maxwell combined his laws of electricity and magnetism, he found that electromagnetic waves must travel through vacuum at a speed fixed entirely by two constants of free space:
c=μ0ε01
where
ε0=8.85×10−12C2N−1m−2 is the permittivity of free space, and
μ0=4π×10−7T m A−1 is the permeability of free space.
Plugging in these numbers gives c≈3×108 m/s — matching the measured speed of light. This agreement was the decisive clue that light itself is an electromagnetic wave.
Key Properties
Same for all electromagnetic waves. Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays all travel at c in vacuum, regardless of their frequency or wavelength.
Universal constant. In vacuum, c is the same for every observer and does not depend on the motion of the source — the starting postulate of Einstein's special relativity.
The cosmic speed limit. No material object or signal carrying information can travel faster than c.
Links wavelength and frequency. For any EM wave in vacuum,
c=fλ
so a high-frequency wave has a short wavelength and vice versa.
Speed of Light in a Medium
Inside a transparent material (glass, water, etc.) light slows down. Its speed becomes
v=nc=με1
where n=μrεr is the refractive index of the medium and is always greater than 1. For example, in water n≈1.33, so light travels at about 2.25×108 m/s. The frequency stays the same, but the wavelength shortens because v=fλ. …
Why this formula?
Speed of Light: Why the Formula Holds
The speed of light (c) is not just a number — it emerges from the fundamental laws of electricity and magnetism. Let's understand why its value is fixed and where the formula comes from.
1. The Core Formula
The speed of light in vacuum is given by:
c=μ0ε01
Where:
μ0 = permeability of free space (how easily a magnetic field forms)
ε0 = permittivity of free space (how easily an electric field forms)
2. Why This Formula? — The Derivation
Step 1: Maxwell's Equations
James Clerk Maxwell unified electricity and magnetism into four equations. Two key ones for light:
Faraday's Law: A changing magnetic field creates an electric field
∇×E=−∂t∂B
Ampère's Law (with Maxwell's correction): A changing electric field creates a magnetic field
∇×B=μ0ε0∂t∂E
Step 2: The Wave Emerges
Take the curl of Faraday's Law:
∇×(∇×E)=−∂t∂(∇×B)
Using the vector identity ∇×(∇×E)=∇(∇⋅E)−∇2E and noting that in vacuum ∇⋅E=0, we get:
−∇2E=−∂t∂(∇×B)
Now substitute Ampère's Law for ∇×B:
−∇2E=−∂t∂(μ0ε0∂t∂E)
Step 3: The Wave Equation
This simplifies to:
∇2E=μ0ε0∂t2∂2E
This is the wave equation. For any wave, the general form is:
∇2E=v21∂t2∂2E
Comparing the two, the wave speed v must satisfy:
v21=μ0ε0
Hence:
v=μ0ε01
This v is the speed of light — denoted c.
3. Why Is It Constant?
μ0 and ε0 are fundamental constants of nature — they don't depend on the observer or the source.