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The Index of refraction is defined as "The ratio of the angle of incidence of one medium with respect to the angle of refraction of another medium."

or in terms of Snell's Law it can be defined as:

The ratio of the sine of the angle of incidence to the sine of the angle of refraction.

It is given by, 

η = sini/sinr

where, 

i is the Angle of Incidence 

r is the Angle of refraction.

It is constant for a pair of specific media and is known as the index of refraction of the second medium with respect to the first medium. 

Index of refraction is represented by the Greek letter µ (mu) or by the alphabet 'n'. 

Let us consider a light ray AO crossing from medium 1 to medium 2 at a point O of the interface between the mediums. Suppose the mediums are similar in nature, then the incident ray AO would have continued straight and would have emerged out as ray OA' in the second medium. But due to change in nature of medium, the ray drifts by certain angle from the straight line path emerges as ray OB. This ‘drifting’ of the emergent light ray is called as ‘Refraction’ of the light ray. 

It is not always that the emerging ray refracts to the left as shown in the diagram. It can be to the right as well, depending upon the inter relations between the nature of the mediums.

The amount of refraction of the light ray is also dependent of the nature of the second medium and measured by a factor called ‘Index of refraction’ of the medium.

The Index of refraction of a medium (n) is defined as the ratio of velocity of light in vacuum (c) to its velocity in that medium (v).

In other words, 

n = cv.

In Parallel, the refraction of a wave across two mediums is found to obey a law, called Snell’s law. 

Referring to the same diagram given above Snell’s Law is mathematically stated as:

sinx/siny = v1/v2

where, v1 and v2 are the phase velocities of the ray in medium 1 and medium 2 respectively. 

Now from our definition of index of refraction in terms of velocities, we can write,

v1/v2 = n2/n1

where, n1 and n2 are the index of refraction of medium 1 and medium 2 respectively. 

∴ sin(x)/sin(y) = n2/n1

Which is the index of refraction equation which can be used to find an index of refraction of a medium experimentally.

From the Index of Refraction Formula it may be noted that the angle ‘y’ will be greater if n2 < n1. That is, the refracted ray bends away from the normal if a light ray enter a less dense medium from a higher denser medium.