Rayleigh criterion
● VERBATIM — examined word-for-wordTwo images are just resolved when the central maximum of the diffraction pattern of one coincides with the first minimum of the diffraction pattern of the other. For an aperture of width b this gives a minimum angular separation θ ≈ λ/b; sources separated by more than this are well resolved, and by less are unresolved.
θ_min ≈ λ/b · just resolved when angular separation = θ_min · linear separation y ≈ D θ_minWhat this actually means
Learn the statement word for word: central maximum of one falls on the first minimum of the other. Vague answers about the patterns just overlapping earn nothing.
It follows directly from sin θ = λ/b with the small-angle approximation, so it is not a new physics idea, only a new use of the single-slit result.
Resolution improves with a larger aperture or a shorter wavelength. That is why research telescopes have huge mirrors and why electron microscopes beat optical ones: the de Broglie wavelength of an electron is thousands of times smaller than that of visible light.
The standard calculation compares two angles. Work out θ_min = λ/b, then work out the actual angular separation of the sources as y/D, then say whether the actual separation is greater or less than θ_min and conclude.
For a circular aperture the true constant is 1.22λ/D, but the 9749 syllabus treats all apertures as rectangular slits, so use θ ≈ λ/b unless told otherwise.
Describing just resolved as the two patterns merely overlapping, without naming the central maximum and first minimum.
Prove it — watch it be true
- Open the Rayleigh criterion view showing two overlapping diffraction patterns.
- Slide the sources together until the alignment marker shows the central maximum of one sitting on the first minimum of the other, and read the angle.
- Confirm that angle equals λ/b, then reduce b and watch the just-resolved angle grow.