Radiance is also sometimes called intensity, especially by astronomers and astrophysicists, and in heat transfer. This can cause confusion in optics, where intensity can mean any of radiant intensity, luminous intensity or irradiance, depending on the background of the person using the term. In photometry and radiometry intensity has a different meaning: it is the luminous or radiant power per unit solid angle. The intensity should then be defined as the magnitude of the Poynting vector. For example, an evanescent wave may have a finite electrical amplitude while not transferring any power.

The treatment above does not hold for arbitrary electromagnetic fields. I = c n ε 0 2 | E | 2, įor non-monochromatic waves, the intensity contributions of different spectral components can simply be added. This is an example of the inverse-square law.Īpplying the law of conservation of energy, if the net power emanating is constant, If a point source is radiating energy in all directions (producing a spherical wave), and no energy is absorbed or scattered by the medium, then the intensity decreases in proportion to the distance from the object squared. For example, the intensity of an electromagnetic wave is proportional to the square of the wave's electric field amplitude. The intensity of a wave is proportional to the square of its amplitude. The resulting vector has the units of power divided by area (i.e., surface power density). Intensity can be found by taking the energy density (energy per unit volume) at a point in space and multiplying it by the velocity at which the energy is moving. The word 'intensity' as used here is not synonymous with ' strength', ' amplitude', ' magnitude', or ' level', as it sometimes is in colloquial speech. For example, one could calculate the intensity of the kinetic energy carried by drops of water from a garden sprinkler. Intensity can be applied to other circumstances where energy is transferred. Intensity is used most frequently with waves such as acoustic waves ( sound) or electromagnetic waves such as light or radio waves, in which case the average power transfer over one period of the wave is used. In the SI system, it has units watts per square metre (W/m 2), or kg⋅ s −3 in base units. In physics, the intensity or flux of radiant energy is the power transferred per unit area, where the area is measured on the plane perpendicular to the direction of propagation of the energy. For other uses, see Intensity (disambiguation). Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, The height of the bulb installation and the presence or absence of the lampshade have a great influence on the light intensity.

Want to cite, share, or modify this book? This book uses the This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. The wave energy is determined by the wave amplitude.

In electromagnetic waves, the amplitude is the maximum field strength of the electric and magnetic fields ( Figure 16.10). If some energy is later absorbed, the field strengths are diminished and anything left travels on.Ĭlearly, the larger the strength of the electric and magnetic fields, the more work they can do and the greater the energy the electromagnetic wave carries. Once created, the fields carry energy away from a source. However, there is energy in an electromagnetic wave itself, whether it is absorbed or not. These fields can exert forces and move charges in the system and, thus, do work on them. Other times, it is subtle, such as the unfelt energy of gamma rays, which can destroy living cells.Įlectromagnetic waves bring energy into a system by virtue of their electric and magnetic fields. Sometimes this energy is obvious, such as in the warmth of the summer Sun.

Explain how the energy of an electromagnetic wave depends on its amplitude, whereas the energy of a photon is proportional to its frequencyĪnyone who has used a microwave oven knows there is energy in electromagnetic waves.

Calculate the Poynting vector and the energy intensity of electromagnetic waves.

Express the time-averaged energy density of electromagnetic waves in terms of their electric and magnetic field amplitudes.

By the end of this section, you will be able to:

Average intensity of light equation