Define Miller index, and the recipe for how to find the Miller index for a particular lattice plane

Miller index:

This is the set of number which is used to define the position of face any crystal. We know that crystal plane is the plane where large number of molecule are present inside this plane.

Lets take r is the vector which is passing through the origin of lattice

r = a i + b j + c k

So the intercept on the plane x is a unit, on the y plane is b unit and on the z plane is c unit.

Now when we take the reciprocal of these intercept we get 1/a, 1/b, and 1/c. These reciprocal of intercept is know as Miller index.