Question

Relation between refractive index and group velocity in electromagnetic wave

Answer 1

Light travels as waves, with the wavefronts perpendicular to the direction of motion. In the animation shown here, the wavefronts are represented by the green parallel lines. The red arrow represents the direction of motion.  As light moves from air into water, it not only slows, but the wavelength changes. The animation below illustrates how the wavelength becomes shorter in the denser medium of water. To replay an animation, click on "replay".  Once you have viewed the first animation, click on "2" to continue.


Interestingly enough, the frequency of the waves does not change as the light moves from air to water. As we saw in the Review page, the wave's speed v is related to both the frequency f and the wavelength  :
v =  f.

Combining the above expression for velocity with the definition of index of refraction, we find a relationship between the wavelength  = v/f in a medium and the wavelength 0 = c/f in vacuum:


In the above equation, the frequencies cancel because frequency does not change as light moves from one medium to another.