<aside> <img src="https://prod-files-secure.s3.us-west-2.amazonaws.com/369dfa6b-d4d9-4cf2-a446-e369553b6347/38305d51-7149-4855-a95f-fd49e2075e61/Electromagnetic_wave_spectrum.png" alt="https://prod-files-secure.s3.us-west-2.amazonaws.com/369dfa6b-d4d9-4cf2-a446-e369553b6347/38305d51-7149-4855-a95f-fd49e2075e61/Electromagnetic_wave_spectrum.png" width="40px" /> Electromagnetic wave spectrum
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https://www.desmos.com/calculator/r1gyhegl4s
Wavelength $\lambda$ is a distance typically in $\rm nm$ or $\rm \mu m$
It is related to the wave vector $k$
$$ |\vec k|= \frac{2\pi}{\lambda} $$
Frequency $\upsilon$ or $f$ is measured in $\rm Hz$
$$ \upsilon=f\lambda $$
Refractive index
$$ v=\frac{c}{n} $$
🗒️ Note: $n \ge 1$ but can be complex
light momentum
$$ |\vec p |=\frac{h}{\lambda} $$
<aside> <img src="https://prod-files-secure.s3.us-west-2.amazonaws.com/369dfa6b-d4d9-4cf2-a446-e369553b6347/e2a3328d-c68b-4f39-bb5f-686389e9e652/Radiometric.png" alt="https://prod-files-secure.s3.us-west-2.amazonaws.com/369dfa6b-d4d9-4cf2-a446-e369553b6347/e2a3328d-c68b-4f39-bb5f-686389e9e652/Radiometric.png" width="40px" /> Radiometric: direct measure of the energy or power (and related quantities).
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<aside> <img src="https://prod-files-secure.s3.us-west-2.amazonaws.com/369dfa6b-d4d9-4cf2-a446-e369553b6347/04940448-4c6e-42ff-9a6f-fc5b5083027b/Photometric.png" alt="https://prod-files-secure.s3.us-west-2.amazonaws.com/369dfa6b-d4d9-4cf2-a446-e369553b6347/04940448-4c6e-42ff-9a6f-fc5b5083027b/Photometric.png" width="40px" /> Photometric: measure of the effective energy or power as seen by the human eye, it takes into account the response of the eye.
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| Definition | Radiometry | Unit | Photometry | Unit | |
|---|---|---|---|---|---|
| $\phi$ | Optical flux (total power emitted in all directions) | Radiation Flux | $\rm W$ (Watt) | Luminous Flux | $\rm lm$ (lumens) |
| $E$ | Flux per unit area (from the whole hemisphere above) $E=\frac{\text d \phi}{\text dA}$ | Irradiance | $\rm Wm^{-2}$ | Illuminance | $\rm lm \, m^{-2}$ or $\rm lx$ (lux) |
| $I$ | Flux per unit steradian | ||||
| $I=\frac{\text d \phi}{\text d \Omega}$ | Radiant | ||||
| Intensity | $\rm W \, sr^{-1}$ | Luminous Intensity | $\rm cd$ | ||
| (candela SI base unit) | |||||
| $L$ | Light emitted from part of an extended source into a | ||||
| particular solid angle | |||||
| $L=\frac{\text d^2 \phi}{\text d \Omega \text d A\cos(\theta)}$ | Radiance | $\rm W \, sr^{-1} \, m^{-2}$ | Luminance | $\rm cd \, m^{-2}$ |
The perceived radiation flux by the human eye is
$$ \phi_\upsilon = K \int V(\lambda) \phi_e(\lambda) \,\text d \lambda $$
where:
🗒️ Note: There are 3 versions of $V(\lambda)$, $V(\lambda)$ for bright light $V(\lambda)'$ for dark light and another one in an intermediate state
$\vec E$ and $\vec B$ are vectors at right angles to the propagation direction $\vec z$
