A small circular disk is illuminated by coherent monochromatic light. A screen is placed a short distance behind the disk — well within the near-field region. Wave optics predicts what at the geometric center of the disk's shadow?
AA bright spot, because wavelets diffracting around the entire rim of the disk travel nearly equal path lengths and interfere constructively
BComplete darkness, matching the geometric shadow
CA pattern identical to the far-field Fraunhofer diffraction from a circular aperture
DA dark fringe, because the disk blocks the central Fresnel zone
This is the Poisson (Arago) bright spot: all the edge wavelets travel nearly equal distances to the geometric center of the shadow, so they arrive in phase and interfere constructively — producing a bright spot exactly where geometric optics predicts darkness. Option 1 is the geometric-optics intuition that Fresnel diffraction directly contradicts. The bright spot was confirmed experimentally in 1818 and became a landmark test of wave optics.
Question 2 Multiple Choice
The Fresnel zone construction divides a wavefront into concentric rings so that consecutive zones contribute path lengths differing by λ/2. What is the consequence for the total amplitude at the observation point?
AContributions from odd-numbered zones interfere constructively with each other, while even-numbered zones tend to cancel them — so the total amplitude depends on how many zones are uncovered by the aperture
BAll zones contribute equally in phase, so amplitude increases without limit as more zones are exposed
COnly the innermost zone contributes significantly; outer zones are negligible due to their large angle of incidence
DFresnel zones only apply when the aperture diameter is smaller than one wavelength
Because adjacent zones are λ/2 apart in path length, they arrive roughly out of phase with each other. Odd zones add constructively to the amplitude and even zones subtract. The total amplitude at a point is therefore sensitive to whether an even or odd number of zones is exposed — which is why a small aperture can actually produce a brighter spot than an open wavefront (if it exposes exactly one zone). This has no analog in geometric optics.
Question 3 True / False
The intensity at the geometric center of a circular aperture in Fresnel diffraction can exceed the unobstructed (no aperture) intensity, depending on the aperture size and distance.
TTrue
FFalse
Answer: True
If the aperture exposes exactly one Fresnel zone, the amplitude at the center is roughly twice the unobstructed amplitude, giving four times the unobstructed intensity. This counterintuitive result — an aperture that increases intensity — follows directly from the zone construction: the full wavefront has contributions from all zones that partially cancel, whereas a single exposed zone avoids that cancellation. Fraunhofer (far-field) diffraction does not produce this effect.
Question 4 True / False
Fresnel diffraction reduces to Fraunhofer diffraction when the source and observation point are very close to the aperture.
TTrue
FFalse
Answer: False
The relationship is the opposite. Fraunhofer diffraction is the far-field limit — it applies when source and observation screen are far from the aperture (or equivalently, when lenses are used to collimate and focus the light). Fresnel diffraction is the near-field regime, valid when the observation distance is comparable to or smaller than a²/λ (where a is the aperture size). Moving the screen closer to the aperture does not simplify the analysis; it enters the Fresnel regime where wavefront curvature must be accounted for.
Question 5 Short Answer
Why does a bright spot appear at the center of a circular obstacle's geometric shadow in coherent light, and why does this result contradict geometric optics?
Think about your answer, then reveal below.
Model answer: All diffracted wavelets originating from around the rim of the circular obstacle travel nearly equal path lengths to the center of the geometric shadow, so they arrive approximately in phase and interfere constructively — producing a bright spot. Geometric optics predicts darkness there because it treats light as straight rays blocked by the obstacle. The bright spot is possible only because light is a wave: it bends around the obstacle's edge, and the phase coherence of the rim wavelets produces constructive interference at precisely the location where geometric reasoning expects maximum shadow.
This is the Poisson (Arago) bright spot, named because Poisson derived it as a seemingly absurd prediction of Fresnel's wave theory — and Arago confirmed it experimentally. It illustrates the core insight of Fresnel diffraction: near-field intensity patterns are governed by interference of curved wavefronts, not by geometric shadow boundaries, and the result can be qualitatively opposite to the geometric prediction.