= Circular-aperture diffraction laboratory experiment
An actual teaching setup is described in <Laboratory Exercise No. 4: Diffraction, MIT 6.237, Fall 2024>, for MIT's 6.237 Modern Optics Project Laboratory, Fall 2024. Preparation includes predicting the aperture-size dependence and the distinction between <Fraunhofer diffraction> and <Fresnel diffraction>. A helium–neon <laser> supplies $632.8\,\mathrm{nm}$ <light>; the far-field setup uses a planar incident <wavefront>, a diffracting object and a distant screen, with beam expansion when needed. Figure 1 also marks an optional <CCD> camera. Exercise 4.7 asks students to sketch the circular-aperture pattern, measure the <Airy disk> diameter between correctly identified boundaries, and infer the aperture size. No measured values are supplied. As a regime comparison, exercise 4.9 varies the circular opening's position near a microscope objective <optical lens>, observes near-field patterns and compares them with the far-field case. This tests whether a change in propagation geometry changes the pattern. The coherent illumination measures one aperture's response, rather than the discrimination of two mutually incoherent <optical point sources>.<Laboratory Exercise No. 4: Diffraction, MIT 6.237, Fall 2024>[pp. 1–2, introduction, PL4.1 and Fig. 1; p. 5, §4.7; p. 6, §4.9: apparatus, readout and regime comparison]{ref}
For a quantitative interpretation, let $L$ be the aperture-to-screen distance and $d_{\rm spot}$ the first-zero diameter on the screen. In the <paraxial approximation>, the independent calculation is
$$
d_{\rm spot}\simeq2L\theta_1=2\frac{j_{1,1}}\pi\frac{\lambda L}{D},\qquad D\simeq2\frac{j_{1,1}}\pi\frac{\lambda L}{d_{\rm spot}}.
$$
For an explicitly hypothetical measurement, $L=1.80\,\mathrm m$ and $d_{\rm spot}=5.60\,\mathrm{mm}$ at $632.8\,\mathrm{nm}$ would imply $D\simeq0.496\,\mathrm{mm}$. The scale $D^2/\lambda\simeq0.389\,\mathrm m$ is smaller than $L$, but only by a factor of about $4.6$; this alone gives limited confidence in a high-precision <Fraunhofer diffraction> approximation. It is not a reported MIT measurement.
Additional recommended controls are to keep <wavelength> fixed, record $L$, centre and uniformly illuminate the <aperture>, and repeat with another $D$. Compare $d_{\rm spot}/L$, which should vary inversely with $D$. A camera readout should include blocked-beam background and avoid saturation. A scaled repetition at larger $L$ tests residual <Fresnel diffraction>; nonuniform illumination, <optical aberrations>, detector sampling and uncertainty in locating a dark ring limit the inferred $D$. The screen pattern's apparent bright edge depends on display brightness and is not a substitute for the first-zero boundary.
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