The h,k,l numbers form a vector perpendicular to the h,k,l planes (which are parallel to one another as well). The length of that vector h,k,l is inversely proportional to the space between planes.

So, for h,k,l=1,0,0 : the planes are perpendicular to the

*x* axis and the distance between them is 1.

For h,k,l=2,0,0 : the planes are also perpendicular to

*x* but with an inter-plane distance of 1/2.

For h,k,l=3,0,0 : the inter-plane distance is 1/3.

And so on...

If d

_{hkl} is the distance between planes, then d

_{2h,2k,2l} = d

_{hkl}/2

d

_{3h,3k,3l} = d

_{hkl}/3

and so on....

Now, let's go back to Bragg's law: nλ = 2dsinθ.

First case: n=1 then λ = 2d

_{hkl}sinθ

Second case: n=2 then 2λ = 2d

_{hkl} sinθ

λ = 2(d

_{hkl}/2)sinθ

λ = 2d

_{2h,2k,2l}sinθ

Bragg's law for n=1 and 2h,2k,2l

So, more generally: Bragg's law for n and h,k,l

Bragg's law for n=1 and nh,nk,nl

When you write Bragg's law λ = 2dsinθ, it doesn't mean that the

*n* number is gone. It is just "incorporated" into the

*d*.

See

http://en.wikipedia.org/wiki/Miller_index for more explanation