Speed of Light Calculator (E=mc²)
Apply formulas involving c (speed of light): mass-energy equivalence (E=mc²) and light travel time over a distance.
Speed of light in a medium: v = c / n
In vacuum the speed of light is c = 299,792,458 m/s — an exact value by definition of the SI metre (1983). In a material medium light slows to v = c / n, where n is the medium's refractive index. Typical values: air n ≈ 1.0003 (virtually c), water 1.33, common glass 1.5, diamond 2.42. When light crosses a boundary between media, it bends — refraction — following Snell's law n₁·sin θ₁ = n₂·sin θ₂. Going from a denser medium to a less dense one beyond the critical angle produces total internal reflection, the principle behind optical fibre. When a charged particle travels through a medium faster than light's local speed v (lower than c), it emits the characteristic blue Cherenkov radiation seen around nuclear-reactor cores. Example: in a fibre with n = 1.5, v ≈ 199,861,639 m/s ≈ 200,000 km/s — about 33% slower than in vacuum.
Applications
Optical fibre and telecommunications: data travels at ~200,000 km/s inside the silica core, with critical-angle total internal reflection confining the signal. Optical lenses: refraction at curved surfaces (cameras, glasses, microscopes). Spectroscopy: dispersion in prisms separates wavelengths because n depends on frequency. SI metre definition: the metre is the distance light travels in vacuum in 1/299,792,458 second.
FAQ
Can anything travel faster than c? Not faster than c in vacuum. But a particle can travel faster than light's speed in a medium (v = c/n) — that's exactly what produces Cherenkov radiation.
Why does the refractive index depend on wavelength? Because n depends on how electrons in the material respond to the wave's frequency. This is called dispersion and is what makes a prism separate white light.
How much faster is c than sound? About a million times. Sound in air is ~343 m/s; light in vacuum is ~3×10⁸ m/s — roughly 874,000× faster.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.