Distance b/w two miller planes

[afrano]

I am having a hard time visualizing the distance b/w two Miller planes. I found this article that has a brief explanation:
http://www.mrl.ucsb.edu/~seshadri/2004_100A/100A_MillerBragg.pdf

which derives the common formula for the distance, which can be used for diffraction/crystallography purposes.

Can someone explain how the distance b/w two miller planes boils down to the distance from the origin to the nearest plane?

Thanks

 

[will.c]

Because all miller planes are equally spaced, and there is always one through the origin.