# 強度 (物理)

## 數學描述

$P = \int I\, \cdot dA$,

If one integrates over a surface of uniform intensity I, for instance over a sphere centered around a point source radiating equally in all directions, the equation becomes

$P = |I| \cdot A_\mathrm{surf} = |I| \cdot 4\pi r^2 \,$,

where I is the intensity at the surface of the sphere, and r is the radius of the sphere. ($A_\mathrm{surf} = 4\pi r^2$ is the expression for the surface area of a sphere).

Solving for I gives

$|I| = \frac{P}{A_\mathrm{surf}} = \frac{P}{4\pi r^2}$.

Anything that can transmit energy can have an intensity associated with it. For an electromagnetic wave, if E is the complex amplitude of the electric field, then the time-averaged energy density of the wave is given by

$\left\langle U \right \rangle = \frac{n^2 \epsilon_0}{2} |E|^2$,

and the intensity is obtained by multiplying this expression by the velocity of the wave, $c/n$:

$I = \frac{c n \epsilon_0}{2} |E|^2$,

where n is the refractive index, $c$ is the speed of light in vacuum and $\epsilon_0$ is the vacuum permittivity.

The treatment above does not hold for electromagnetic fields that are not radiating, such as for an evanescent wave. In these cases, the intensity can be defined as the magnitude of the Poynting vector.[1]

## 參閱

[编辑]

[編輯]

（Radiosity） Je or J 瓦特每平方 W⋅m−2 表面出射及反射的辐射通量总和

（Radiant energy density） ωe 焦耳每米3 J⋅m−3
（Radiant intensity） Ie 瓦特球面度 W·sr−1 每單位立體角的辐射通量。

M

W⋅m−3
or
W⋅m−2⋅Hz−1

L

W⋅sr−1m−3

W⋅sr−1⋅m−2Hz−1

Eν

W·m−3

W·m−2·Hz−1

（Spectral intensity） I 瓦特球面度 W⋅sr−1⋅m−1 辐射强度的波长分布

## 參考資料

1. ^ Paschotta, Rüdiger. Optical Intensity. Encyclopedia of Laser Physics and Technology. RP Photonics.