WAV-22

Bragg diffraction

Crystal diffraction.

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GoverningBragg diffraction

Governing equation

n\lambda=2d\sin\theta

$th \in \left[5, 60\right]$

where

n: n (—)
d: d (pm)
th: th (deg)
lam: Bragg diffraction (pm)

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

n\lambda=2d\sin\theta

$th \in \left[5, 60\right]$

$th = 5$ $lam = 34.86$

Along the curve

②

Domain of the variable — blue

th_{\min} = 5,\quad th_{\max} = 60

$th \in \left[5, 60\right]$

$th = 5$ $th = 5$

Along the curve

③

Response curve — green

n\lambda=2d\sin\theta

$th \in \left[5, 60\right]$

$th = 5$ $lam = 34.86$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}lam}{\mathrm{d}th}

$th \in \left[5, 60\right]$

$th = 5.346$ $lam^{\prime} = 6.951$

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-22 — Bragg diffraction) is the form associated with Bragg diffraction. Working symbols: $n$ , $d$ , $th$ $\rightarrow$ $lam$ . Crystal diffraction. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

lam

from

n

d

th

in Waves & optics via

n\lambda=2d\sin\theta

Crystal diffraction. 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

n = 1.000\,\mathrm{—}

d = 200.000\,\mathrm{pm}

th = 20.000\,\mathrm{deg}

, the governing relation

n\lambda=2d\sin\theta

yields

lam = 136.808\,\mathrm{pm}

. 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

n n1 —d d200 pmth th20 deg

Outputs

Bragg diffraction lam136.808 pm

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Narration of this film

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

Crystal diffraction. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube