Physics · Ch 6 — Optics
Fresnel's Distance
Fresnel's Distance
Fresnel's distance is the distance, from a diffracting aperture of width , up to which the rectilinear (straight-line ray) propagation of light remains a good approximation, and beyond which the bending due to diffraction becomes significant and wave optics must be used instead. Using the first-minimum diffraction angle , Fresnel's distance is defined by equating the FULL angular spread of the central maximum, , to the simple geometric angular width the aperture itself subtends at that same distance : , i.e. , which rearranges to . A larger aperture or a shorter wavelength both give a larger Fresnel distance, i.e. ray optics stays valid over a longer range -- which is exactly why, for everyday …
What this figure shows. An aperture of width a is shown with two labelled regions extending away from it: a near region, close in, where the beam still travels essentially in a straight line just as ray optics would predict, and a far region, beyond a marked boundary distance, where the beam has visibly spread out into a cone of half-angle theta due to diffraction and wave-optics effects dominate instead. The marked boundary between these two regions is Fresnel's distance z, found by setting the diffraction-predicted angular spread lambda/a equal to the simple geometric a …
Worked out. An aperture (slit) of width a = 5 mm and light of wavelength 500 nm are given. Substituting into Fresnel's distance formula z = a^2/(2 lambda) gives z = (5e-3)^2/(2 times 500e-9) = 25e-6/(1e-6) = 25 m. The key physical takeaway is that even a modest few-millimetre aperture keeps ray optics valid out to tens of metres, which is why diffraction spreading is not noticed in everyday viewing but becomes important for very narrow slits or very long propagation dis …