Miller Indices Calculator
Visible light is thousands of times too long to diffract from planes this close — hence X-rays.
The formula
d = a / sqrt(h^2 + k^2 + l^2) ; n*lambda = 2 d sin(theta)
Indices are reciprocals
The Miller indices of a plane are the reciprocals of where it cuts the three axes, cleared of fractions. A plane parallel to an axis never cuts it, so that intercept is infinite and its reciprocal is zero — which is why zeros appear so often. The reciprocal convention exists precisely to avoid writing infinity in an index.
Higher indices mean closer planes
The spacing falls as the square root of the sum of squares, so (111) planes are further apart than (222), and (100) further apart than (200). Since Bragg's law needs the wavelength to be no more than twice the spacing, closely spaced planes eventually stop diffracting altogether — and that limit is why X-rays are used rather than visible light.
Where these models stop
Michaelis-Menten assumes a single substrate and a steady state; Langmuir assumes one layer on identical sites with no interaction between them; Stokes-Einstein assumes a hard sphere much larger than the solvent molecules around it. Each is an idealisation that happens to describe real systems well over a useful range, and each fails predictably outside it. Knowing which assumption a number rests on is usually more valuable than the number.