Past exam of the physics A course of the University of Cambridge / 2018 / Paper 2 / Section B / B7 / a

In Fraunhofer diffraction, the relative propagation phase across the aperture is linear in aperture coordinates. If $b$ is its largest transverse size, the neglected quadratic path term must be small: for an observer at distance $R$,For a finite-distance point source a distance $s$ away, also require $b^2/(\lambda s)\ll 1$ if the illumination is to be treated as a plane wave. Numerical factors depend on whether $b$ is a radius or full width and on the permitted phase error; the condition expresses a small Fresnel number.

One can place both source and screen sufficiently far away, or collimate a point source with a lens and observe the aperture in the back focal plane of a second lens. In the latter arrangement rays of each outgoing direction focus at one point, with $X\simeq f{\theta }_x$; the lens removes the need for a physically distant screen. A laser beam approximately uniform across the aperture can supply the incident plane wave. The sketches distinguish an actual far field from its focal-plane equivalent.