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phys: clarify intensity variables

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eggy 2021-01-11 19:08:43 -05:00
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docs/sph3u7.md
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@ -698,7 +698,7 @@ $$E\propto I\propto A^2$$
**Malus's law** states that for a polarised wave of energy $E_0$, the amplitude from the second filter, where $\theta$ is the angle between the polariser and the analyser, such that: **Malus's law** states that for a polarised wave of energy $E_0$, the amplitude from the second filter, where $\theta$ is the angle between the polariser and the analyser, such that:
$$E=E_0\cos\theta$$ $$E=E_0\cos\theta$$
And so: And so, where $I$ is the intensity of the polarised/analysed light, $I_0$ is the intensity of the plane-polarised light, and $\theta$ is the angle between the polariser and the analyser:
$$I=I_0\cos^2\theta$$ $$I=I_0\cos^2\theta$$
When **unpolarised light** passes through a polariser, the average result of $I\cos^2\theta$ is $\frac{1}{2}$, so the intensity of polarised light is **half** of the intensity of unpolarised light. When **unpolarised light** passes through a polariser, the average result of $I\cos^2\theta$ is $\frac{1}{2}$, so the intensity of polarised light is **half** of the intensity of unpolarised light.