Question

How does the refractive index of a medium depend on the velocity of light?

Answer 1

$v = \frac{c}{\lambda}$

=> v is inversely proportional to $\lambda$

$<i><textbf>As wavelength of light decreases, the velocity of light decreases.$

We know,

Absolute refractive index of a medium is ratio of velocity of light in vacuum to velocity of light in that medium.

$n_{m} = \frac{c}{c_{m}}$

So If the velocity of light changes, the refractive index of the medium (for that wavelength of light) also changes.

$<b><i>Example:$

It's due to this difference in velocities that dispersion of sunlight (to form rainbow) takes place.
While rainbow is formed, the different colors (with different wavelengths) bend at different angles, but as all colors of light pass through same medium, thus, refractive index of medium does depend on the wavelengths, which means indirectly depends on velocity of light

Answer 2

Answer:

The lower the refractive index, the faster the velocity of light. Medium A has the smaller refractive index. Light will travel faster through medium A at a velocity equal to the speed of light divided by the refractive index.