List of optics equations

This article summarizes equations used in optics, including geometric optics, physical optics, radiometry, diffraction, and interferometry.

There are different forms of the Poynting vector, the most common are in terms of the E and B or E and H fields.

For spectral quantities two definitions are in use to refer to the same quantity, in terms of frequency or wavelength.

Kinetic momentum:

Canonical momentum:

At a spherical surface:

ε μ

sin ⁡ ( k x − ω t )

Lens focal length from refraction indices

{\displaystyle {\frac {1}{f}}=\left({\frac {n_{\mathrm {lens} }}{{n}_{\mathrm {med} }}}-1\right)\left({\frac {1}{r_{1}}}-{\frac {1}{r_{2}}}\right)\,\!}

Image distance in a spherical mirror

Subscripts 1 and 2 refer to initial and final optical media respectively.

These ratios are sometimes also used, following simply from other definitions of refractive index, wave phase velocity, and the luminal speed equation:

sin ⁡ θ

{\displaystyle A\left(\mathbf {r} \right)\propto \iint _{\mathrm {aperture} }E_{\mathrm {inc} }\left(\mathbf {r} '\right)~{\frac {e^{ik\left|\mathbf {r} -\mathbf {r} '\right|}}{4\pi \left|\mathbf {r} -\mathbf {r} '\right|}}\mathrm {d} x'\mathrm {d} y'}

Far-field (Fraunhofer)

sin ⁡ θ

cos ⁡ ϕ

+ sin ⁡ ϕ

{\displaystyle A\left(\mathbf {r} \right)\propto {\frac {e^{ikr}}{4\pi r}}\iint _{\mathrm {aperture} }E_{\mathrm {inc} }\left(\mathbf {r} '\right)e^{-ik\left[\sin \theta \left(\cos \phi x'+\sin \phi y'\right)\right]}\mathrm {d} x'\mathrm {d} y'}

In astrophysics, L is used for luminosity (energy per unit time, equivalent to power) and F is used for energy flux (energy per unit time per unit area, equivalent to intensity in terms of area, not solid angle).

They are not new quantities, simply different names.

(Bolometric)