# Why phase velocity of light is slower in a dielectric than vacuum?

Why does light speed suffer a reduction when it passes through a homogeneous dielectric medium? I know my math says so, i.e.- a highly polarizable ($\chi$) medium is associated with high $\epsilon$ (=$1+\chi$), and according to Helmholtz equation $\nabla^{2}E+\omega^2\mu\epsilon E=0$, the wavelength $\left(\lambda=\dfrac{2\pi}{\omega\sqrt{\mu\epsilon}}\right)$ should shrink down with larger $\epsilon$, leading to slower phase velocity. But is there any intuitive explanation behind that? Why should a highly polarizable medium (with no scattering) lead to slow speed (or smaller wavelength)?

Let me put my question in some other way. Lets assume, we have a group of identical charged harmonic oscillator arranged along a straight line in air, with a finite spacing between them. No damping is there. This should essentially mimic a $1 D$ lossless dielectric medium. Once the rightmost oscillator is set in motion, it will begin radiation. It radiates in all direction, but for the time being, let's just care about the forward radiation only. This propagating radiation will eventually cause all other oscillator to vibrate and re-radiate. If we can explain how the phase difference between any two neighboring oscillators depends on the polarization amplitude $(P=q\times d)$, $d$ being the distance from equilibrium and $q$ is charge), it should suffice to answer my original question, i.e.- why light speed is slower in dielectric.

• Thanks a lot elifino. However, I appreciate your statement as an annexed information, instead of a direct answer to my question. Its true that, for different frequencies, $\epsilon$ can be smaller than 1 (leading phase velocity greater than lightspeed), equal to zero (longitudinal surface plasmon wave), or even negative. It all depends on how atoms are polarized by electric field. But how will you intuitively explain the phenomenon of reduced phase-velocity of visible light in a typical dielectric, say glass? – Joy Nov 25 '15 at 6:26
• Also, phase-shift of radiated field due to damping/scattering is accounted as loss in dielectric, and has nothing to do with the imaginary part of propagation constant ($\gamma=\alpha +i\beta$). So it does not explain why we have reduced light speed in a lossless medium. – Joy Nov 25 '15 at 6:38