WAV-25

Rayleigh criterion

Circular-aperture resolution.

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GoverningRayleigh criterion

Governing equation

\theta=1.22\lambda/D

$D \in \left[5, 400\right]$

where

lam: lam (nm)
D: D (mm)
th: Rayleigh criterion (urad)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\theta=1.22\lambda/D

$D \in \left[5, 400\right]$

$D = 5$ $th = 134.2$

Along the curve

②

Domain of the variable — blue

D_{\min} = 5,\quad D_{\max} = 400

$D \in \left[5, 400\right]$

$D = 5$ $D = 5$

Along the curve

③

Response curve — green

\theta=1.22\lambda/D

$D \in \left[5, 400\right]$

$D = 5$ $th = 134.2$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}th}{\mathrm{d}D}

$D \in \left[5, 400\right]$

$D = 7.484$ $th^{\prime} = -13.46$

Along the curve

Lecture brief

Historical brief

d’Alembert’s wave equation, Snell, the thin-lens maker, Doppler and Bragg interference are the classical optics-and-sound toolkit. The lab is propagation, image and shift. This sheet (WAV-25 — Rayleigh criterion) is the form associated with Rayleigh criterion. Working symbols: $lam$ , $D$ $\rightarrow$ $th$ . Circular-aperture resolution. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

th

from

lam

D

in Waves & optics via

\theta=1.22\lambda/D

Circular-aperture resolution. Use it when a real waves & optics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

lam = 550.000\,\mathrm{nm}

D = 50.000\,\mathrm{mm}

, the governing relation

\theta=1.22\lambda/D

yields

th = 13.420\,\mathrm{urad}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

lam lam550 nmD D50 mm

Outputs

Rayleigh criterion th13.420 urad

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Circular-aperture resolution. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube