The Rayleigh roughness criterion is a widely used means to estimate the degree of roughness of a considered surface. Considering the phase difference between two rays scattered from separate points of the surface, this is proportional to the roughness ∆h (average deviation from the average surface height ) the cosine of the incident angle and, inversely, on the radiation wavelength (λ). The Rayleight criterion states that a surface can be considered as smooth (mostly reflecting) if the phase difference is less than π/2 radians.
As a consequence, in the case of normal incidence (i.e. θ=0), average roughness of the surface must be less than λ/8 to have an effectively smooth surface. For instance: i) at optical wavelengths (e.g. 0.5 micrometers), surface roughness ∆h must be less than about 60 nm to have a specular reflection. Only certain man-made surfaces (e.g. sheets of glass or metal) may meet such a condition; ii) at VHF radio wavelengths (e.g. 3 m), roughness height need only to be less than about 40 cm. Unlike the previous case, a number of natural surfaces may meet this condition.
It is worth noting that large values of the incident angle may satisfy the criterion more easily as compared with the normal incidence. This means that a moderately rough surface may be effectively smooth at glancing incidence. This condition may be easily experienced when eyes are struck by the glare of reflected sunlight from a low sun over an ordinary road surface. More strict conditions for classifying a surface as a mirror or a diffuser at an established whavelength λ are: ∆hcosθ/λ > 1/8 for a rough surface operating as a diffuser; ∆hcosθ/λ < 1/25 for a smooth surface operating as a mirror.