Why Are Reciprocal Quantities Used to Define Atomic Planes?

[Narcol2000]

Atomic planes are defined as the reciprocal quantities 1/u' , 1/v' and 1/w' transformed to the smallest three integers (here the plane intersects the crystal lattice at the unit-cell axes u'a,v'b and w'c).

My question is, why are reciprocal quantities used? This is something that has bugged me for a very long time... it seems pretty arbitrary to me.

 

[Gokul43201]

It's not arbitrary.

For any general plane described by the equation, ax+by+cz+d=0, verify that the intercepts are given by: -d/a, -d/b and -d/c.

That's the origin of the Miller Indices - they describe the coefficients a,b,c in the equation of the plane (or the direction cosines of its normal).

 

[Narcol2000]

Thanks for the tip, it makes sense now, I just hate learning things without knowing the reason behind it.