WAV-32

Critical TIR angle

Total internal reflection onset.

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GoverningCritical TIR angle

Governing equation

\theta_c=\arcsin(n_2/n_1)

$n1 \in \left[1.1, 2.4\right]$

where

n1: n1 (—)
n2: n2 (—)
tc: Critical TIR angle (deg)

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_c=\arcsin(n_2/n_1)

$n1 \in \left[1.1, 2.4\right]$

$n1 = 1.1$ $tc = 65.38$

Along the curve

②

Domain of the variable — blue

n1_{\min} = 1.1,\quad n1_{\max} = 2.4

$n1 \in \left[1.1, 2.4\right]$

$n1 = 1.1$ $n1 = 1.1$

Along the curve

③

Response curve — green

\theta_c=\arcsin(n_2/n_1)

$n1 \in \left[1.1, 2.4\right]$

$n1 = 1.1$ $tc = 65.38$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}tc}{\mathrm{d}n1}

$n1 \in \left[1.1, 2.4\right]$

$n1 = 1.108$ $tc^{\prime} = -108.4$

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-32 — Critical TIR angle) is the form associated with Critical TIR angle. Working symbols: $n1$ , $n2$ $\rightarrow$ $tc$ . Total internal reflection onset. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

tc

from

n1

n2

in Waves & optics via

\theta_c=\arcsin(n_2/n_1)

Total internal reflection onset. 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

n1 = 1.500\,\mathrm{—}

n2 = 1.000\,\mathrm{—}

, the governing relation

\theta_c=\arcsin(n_2/n_1)

yields

tc = 41.810\,\mathrm{deg}

. 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

n1 n11.5 —n2 n21 —

Outputs

Critical TIR angle tc41.810 deg

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Narration of this film

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

Total internal reflection onset. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube