What is the effect of increasing the refractive index of a medium on the speed of light in that medium?

Increasing the refractive index of a medium results in a decrease in the speed of light when it passes through that medium. The refractive index is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. Mathematically, this relationship can be expressed as:

[ n = \frac{c}{v} ]

where ( n ) is the refractive index, ( c ) is the speed of light in a vacuum, and ( v ) is the speed of light in the medium. As the refractive index increases, the value of ( v ) must decrease to maintain the equality since ( c ) is a constant.

Therefore, when light enters a medium with a higher refractive index, it interacts more with the atoms in that medium, which leads to a lower velocity of light compared to its speed in a vacuum. This understanding is foundational in optics and is crucial for interpreting phenomena such as refraction and the bending of light as it passes from one medium into another.