Speed of Light
The speed of light in vacuum, denoted by c, is a universal physical constant equal to exactly 299,792,458 metres per second, representing the maximum speed at which any information, energy, or matter can travel in the universe. As established by Albert Einstein's special theory of relativity (1905), c is invariant regardless of the motion of the source or observer. In transparent media such as glass or water, light travels at a reduced speed given by v = c/n, where n is the refractive index of the medium.
Key Formula
c = 1 / √(μ₀ × ε₀)
LaTeX: c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}
| Symbol | Meaning | Unit |
|---|---|---|
| c | Speed of light in vacuum | m/s |
| μ₀ | Permeability of free space (4π × 10⁻⁷) | H/m or T·m/A |
| ε₀ | Permittivity of free space (8.854 × 10⁻¹²) | F/m |
Worked Example
Problem
Light travels from vacuum into glass with refractive index n = 1.5. Calculate the speed of light inside the glass and the time taken to cross a glass slab 30 cm thick.
Solution
Step 1: Calculate speed in glass. v = c / n = (3 × 10⁸) / 1.5 = 2 × 10⁸ m/s Step 2: Calculate time to cross slab (distance = 30 cm = 0.30 m). t = distance / speed = 0.30 / (2 × 10⁸) t = 1.5 × 10⁻⁹ s
Answer
Speed in glass = 2 × 10⁸ m/s; Transit time = 1.5 ns
Speed of Light in Various Media
| Medium | Refractive Index (n) | Speed (× 10⁸ m/s) | Approximate Speed |
|---|---|---|---|
| Vacuum | 1.000 | 2.998 | 3.00 × 10⁸ m/s |
| Air (STP) | 1.0003 | 2.997 | ≈ 3.00 × 10⁸ m/s |
| Water | 1.333 | 2.249 | ≈ 2.25 × 10⁸ m/s |
| Crown Glass | 1.520 | 1.972 | ≈ 1.97 × 10⁸ m/s |
| Diamond | 2.417 | 1.240 | ≈ 1.24 × 10⁸ m/s |
Interactive Tools
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Related Terms
Refractive Index
The refractive index (n) of a medium is a dimensionless number that describes how much slower light travels through that medium compared to its speed in a vacuum, defined as the ratio of the speed of light in vacuum to the speed of light in the medium. It also quantifies how much a ray of light bends (refracts) when entering the medium from vacuum, as described by Snell's Law. The refractive index determines critical phenomena such as total internal reflection, the sparkle of gemstones, and is essential in designing optical fibres, lenses, and camera systems.
Light Diffraction
Light diffraction is the bending and spreading of light waves around obstacles or through narrow openings, occurring when the size of the aperture or obstacle is comparable to the wavelength of light. It is a consequence of the wave nature of light and produces characteristic interference patterns of alternating bright and dark fringes. Diffraction is fundamental to technologies such as diffraction gratings, X-ray crystallography, CD/DVD data storage, and optical microscopy resolution limits.
Photoelectric Effect
The photoelectric effect is the emission of electrons from a metal surface when light of sufficient frequency strikes it, demonstrating that light behaves as discrete packets of energy called photons rather than as a continuous wave. Albert Einstein explained this phenomenon in 1905 using Max Planck's quantum theory, for which Einstein was awarded the Nobel Prize in Physics in 1921. The effect is the foundation of photovoltaic cells, photodiodes, photomultiplier tubes, and modern solar energy technology.
From Old English "leoht" (light) and Old English "speed" (success, swiftness). The symbol c comes from the Latin "celeritas" (swiftness). The first quantitative measurement was made by Ole Rømer in 1676 using observations of Jupiter's moon Io.