Resolving Power

Suppose that we project the image of two adjacent slits each width d on a screen. If the diffraction patterns are broad enough to overlap, one cannot identify the distributions produced by each separate slit. Generally one cannot separate two sources if the central maxima overlap. The Rayleigh criterion for separating the images of two slits is given by

\[ \rm \mathbf{ \theta_{min}= \frac{\lambda}{d}} \]

If one illuminates a circular aperture of diameter d, a diffraction pattern consisting of a bright central spot surrounded by bright rings is created as shown in the illustration. To separate the images of two adjacent circular apertures, the Rayleigh criterion becomes

\[ \rm \mathbf{ \theta_{min}= \frac{1.22 \lambda}{d}} \]

The ability of a camera or telescope to take photographs of small objects is limited by the Rayleigh criterion where the diameter of the aperture is given by the diameter of the lens.