WAV-23

Thin-film 2nt

Constructive film path.

Reading speed

GoverningThin-film 2nt

Governing equation

2 n t=m\lambda

$t \in \left[50, 800\right]$

where

n: n (—)
t: t (nm)
m: m (—)
lam: Thin-film 2nt (nm)

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

2 n t=m\lambda

$t \in \left[50, 800\right]$

$t = 50$ $lam = 140$

Along the curve

②

Domain of the variable — blue

t_{\min} = 50,\quad t_{\max} = 800

$t \in \left[50, 800\right]$

$t = 50$ $t = 50$

Along the curve

③

Response curve — green

2 n t=m\lambda

$t \in \left[50, 800\right]$

$t = 50$ $lam = 140$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}lam}{\mathrm{d}t}

$t \in \left[50, 800\right]$

$t = 54.72$ $lam^{\prime} = 2.8$

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-23 — Thin-film 2nt) is the form associated with Thin-film 2nt. Working symbols: $n$ , $t$ , $m$ $\rightarrow$ $lam$ . Constructive film path. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

lam

from

n

t

m

in Waves & optics via

2 n t=m\lambda

Constructive film path. 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 = 1.400\,\mathrm{—}

t = 250.000\,\mathrm{nm}

m = 1.000\,\mathrm{—}

, the governing relation

2 n t=m\lambda

yields

lam = 700.000\,\mathrm{nm}

. 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 n1.4 —t t250 nmm m1 —

Outputs

Thin-film 2nt lam700.000 nm

Reading speed

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Narration of this film

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

Constructive film path. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube