Question

What is the unit for the index of refraction?

Answer 1

The bending of a ray of light as it passes through one medium and through another is measured by the refractive index, also known as the index of refraction. In optics, a material's refractive index is a dimensionless number that defines how quickly light passes through it.

Complete answer:
The bending of a ray of light as it passes through one medium and through another is measured by the refractive index, also known as the index of refraction.
In optics, a material's refractive index is a dimensionless number that defines how quickly light passes through it.
It is defined as, $n = \dfrac{c}{v}$
v is the phase velocity of light in the medium, and c is the speed of light in vacuum.
Air, for example, has a refractive index of 1.333, which means light flows 1.333 times slower in water than in air. As the refractive index of a material is increased, the speed of light in the material decreases.
If I is the angle of incidence of a ray in vacuum (the angle between the incoming ray and the perpendicular to the surface of a medium, called the normal), and r is the angle of refraction (the angle between the ray in the medium and the normal), the refractive index n is known as the ratio of the sine of the angle of incidence to the sine of the angle of refraction.
$n = \dfrac{{\sin i}}{{\sin r}}$
The index of refraction has no units because it is just a ratio. The ratio of the speed of light in vacuum to the speed of light in the medium is the refractive index of a medium. It doesn't have any units. It's a measure of the velocity of light in a medium vs the velocity of light in space, with all units of velocity balanced out with only the ratio's amount remaining. The refractive index is the product of these two ratios.

Note:
If I is the angle of incidence of a ray in vacuum (the angle between the incoming ray and the perpendicular to the surface of a medium, called the normal), and r is the angle of refraction (the angle between the ray in the medium and the normal), the refractive index n is known as the ratio of the sine of the angle of incidence to the sine of the angle of refraction.