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...
is the distance between planes, then d2h,2k,2l
and so on....
Now, let's go back to Bragg's law: nλ = 2dsinθ.
First case: n=1 then λ = 2dhkl
Second case: n=2 then 2λ = 2dhkl
λ = 2(dhkl
λ = 2d2h,2k,2l
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
for more explanation