Speed of EM waves in a medium — refraction

What just happened?

The EM wave entered the medium from vacuum and slowed down. In vacuum every electromagnetic wave travels at speed $c$, but inside matter it interacts with its atoms and travels slower — the more so, the larger the refractive index.

Speed of the EM wave in a medium:

— where $c \approx 3\cdot10^8\,\mathrm{m/s}$ is the speed of light in vacuum, and $n \ge 1$ is the refractive index of the medium. The larger $n$, the smaller $v$.

What does it mean in practice?

The frequency $f$ of the wave does not change (the source sets it), so since $v = f\lambda$ decreases, the wavelength shrinks:

That is why in the animation the wavefronts inside the medium are packed more densely than in vacuum — a visible “trace” of the slower speed.

Why does light refract?

A change of speed at the boundary between media changes the direction of the ray — that is refraction (Snell’s law). A larger $n$ = a slower wave = stronger refraction. Diamond ($n=2.42$) slows and bends light strongly, hence its sparkle.

Why you need this for the exam:

The formula $v = c/n$ plus a constant frequency and $\lambda = \lambda_0/n$ solve most problems about light in media. Trick: remember that on entering a medium v and λ change, but not f.

Remember: in vacuum every EM wave travels at speed c; in a medium v = c/n < c — the more optically dense the medium, the slower it goes and the shorter the wave.