Speed of Light Calculator (E=mc²)

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.