WAV-21

Malus law

Polarizer intensity.

Reading speed

GoverningMalus law

Governing equation

I=I_0\cos^2\theta

$th \in \left[0, 90\right]$

where

I0: I0 (W/m²)
th: th (deg)
I: Malus law (W/m²)

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.

00:0 / 00:08

①

Governing law — red

I=I_0\cos^2\theta

$th \in \left[0, 90\right]$

$th = 0$ $I = 1$

Along the curve

②

Domain of the variable — blue

th_{\min} = 0,\quad th_{\max} = 90

$th \in \left[0, 90\right]$

$th = 0$ $th = 0$

Along the curve

③

Response curve — green

I=I_0\cos^2\theta

$th \in \left[0, 90\right]$

$th = 0$ $I = 1$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}I}{\mathrm{d}th}

$th \in \left[0, 90\right]$

$th = 0.566$ $I^{\prime} = -3.45\times 10^{-4}$

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-21 — Malus law) is the form associated with Malus law. Working symbols: $I0$ , $th$ $\rightarrow$ $I$ . Polarizer intensity. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

I

from

I0

th

in Waves & optics via

I=I_0\cos^2\theta

Polarizer intensity. 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

I0 = 1.000\,\mathrm{W/m^{2}}

th = 30.000\,\mathrm{deg}

, the governing relation

I=I_0\cos^2\theta

yields

I = 0.750\,\mathrm{W/m^{2}}

. 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

I0 I01 W/m²th th30 deg

Outputs

Malus law I0.750 W/m²

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

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

Polarizer intensity. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube