Additional item: They would actually do better to teach and emphasize the fundamentals than to just present the formulas. The Rayleigh criteria comes from the result that a faraway point source will create a diffraction pattern upon being incident and focused by the lens in the focal plane so that it focuses to a circular spot/blob instead of a point that covers a ## \Delta \theta \approx 1.22 \frac{\lambda}{D} ##. (I believe this is the ## \theta ## measured from straight on to the first zero of the diffraction intensity pattern (the Airy disc), so that the blob has radius ## r=f (1.22) \frac{\lambda}{D} ##, and the diameter of the blob is ## d=f (2.44) \frac{\lambda}{D} ##). A second faraway (small=point size type) object that is located an angle ## \theta_o ## from the first object will come to a focus, also with a similar circular blob, in the focal plane of the lens, at an angle of ## \theta_o ## away from the center of the first blob, which is a distance ## d_1=f \theta_o ## from center of the first blob. The question is, how big does ## \theta_o ## need to be to tell that we have two separate blobs as opposed to a single blob? (Oftentimes, the answer is given as ## \theta_o=2 \, \Delta \theta = 2.44 \frac{\lambda}{D} ##). Or alternatively, given ## \theta_o ##, how big does the lens diameter ## D ## need to be to make each blob (which is a diffraction pattern also known as an Airy disc) small enough, that we can basically see that there are two distinct blobs. ## \\ ## Given the formula, anyone can do a little arithmetic, but it has been my experience that only a limited number of students are able to pick up the details of this concept, because they often are not presented with enough of the details. ## \\ ## One additional detail: The circular aperture of the lens basically creates a circular diffraction pattern from a single faraway point source that could be viewed in the far-field if it were just an aperture and not a lens. The lens makes it so that the far-field diffraction pattern is brought to a focus and can be viewed in the focal plane of the lens, instead of needing to view it in the far-field. This is because parallel rays that are incident on the lens at angle ## \theta ## come to a focus at a position ## x=f \, \theta ## in the focal plane. (You can think of it as the rays\wavefront from the source first encounter the circular aperture, and then the lens, placed just after the aperture, brings the far field diffraction pattern into view in the focal plane of the lens if a screen is placed there). The far-field pattern from the circular aperture is a diffraction pattern that has a spread (angular distance to off-center to the first zero of the diffraction pattern) ## \Delta \theta ##. The larger the aperture the narrower the angular spread of this circular (Airy disc) pattern. So, instead of the point source focusing to a point, it instead makes a finite sized blob. A second point source needs to be far enough from the first source that the result isn't two overlapping blobs that looks like one blob. ## \\ ## Edit: And a google of the topic "Rayleigh criteria" suggests that 1.22 and not 2.44 is the number to use here.
