We all know the resolution depends on wavelength. However, when a student sees this concept for the first time it does seem paradoxical. After all, the direction in which the wavelength is measured is orthogonal to the transverse dimension of the object we are trying to resolve!
Any ideas what is the simplest and best mental picture to give a student to help resolve the mental conflict caused by this orthogonality?
You cannot image something without some waves being non-perpendicular. If they were, you would just see a flat image with no detail. It is the off-axis rays that give images their detail. So how fine can details be resolved in an image? The minimum feature size occurs when you have two waves travelling parallel to the image plane in opposite directions. The interference they produce is on the order of a wavelength. This can be made a little better by throwing in some additional waves at different angles.
Does this make sense?
You cannot image something without some waves being non-perpendicular. If they were, you would just see a flat image with no detail. It is the off-axis rays that give images their detail. So how fine can details be resolved in an image? The minimum feature size occurs when you have two waves travelling parallel to the image plane in opposite directions. The interference they produce is on the order of a wavelength. This can be made a little better by throwing in some additional waves at different angles.
Does this make sense?
Both @Raymond's and @Baptiste's answers are good and get to the point - especially in the canonical regime of diffraction limited optics. Personally, I think that @Raymond's is the best insight for a conceptual student, because it gets across the need to the spatial information perpendicular to the optical axis, and hence the fact something more than plane waves are required (note that if we are considering fluorescence imaging, then the spatial symmetry breaking is provided by the source).
Alternatively, Baptiste's point about the Airy function is the mathematical description, and works both in emission and reflection: I know many students who will ONLY accept an answer such as this, grumbling about plane waves as not being rigorous enough ;).
There are a few other points of view that you may wish to consider, all of which are entirely complementary.
From a quantum mechanical point of view, you can also motivate this from the cross section of interaction between an individual photon and the object of interest, and that the minimum that this spatial extent can be is given by the wavelength (it can always be larger, based on the coherence length, of course).
And you can motivate this from an information theoretical basis, which then reduces to @Baptiste's response, but which can then be used as a motivation to explore how the use of additional information or physical responses in the form of nonlinear optical effects can be used to get diffraction unlimited imaging.
So to return to your question - just as with the responses, I'd start by giving Raymond's answer, and then quantify with Baptiste's - if you want to extent it with mine, then that's entirely up to you ;).
Any insight on acoustic wave imaging and its relationship to wavelnegth- particularly, if you have to explained- ultrasound propgation and limits to resolution in a swept frequency manner. Thanks a lot for starting this discussion.
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