Black and Grey Surfaces

By Mallesham Devasane|Updated : January 5th, 2017

A black body is defined as a body which absorbs all incident radiation regardless of wavelength and direction.

Within the visual band of radiation, any material, which absorbs all visible light, appears as black. Extending this concept to the much broader thermal band, we speak of surfaces with α = 1 as also being “black” or “thermally black”. It follows that for such a surface, ε = 1 and the surface will behave as an ideal emitter. The terms ideal surface and black surface are used interchangeably.


  • A black, or ideal surface, will have no surface resistance:

16-Black-and-grey-surfaces (1)

In this case the nodal Radiosity and emissive power will be equal.

This result gives some insight into the physical meaning of a black surface. Ideal surfaces radiate at the maximum possible level. Non-black surfaces will have a reduced potential, somewhat like a battery with a corroded terminal. They therefore have a reduced potential to cause heat/current flow.

  • Large surfaces: Surfaces having a large surface area will behave as black surfaces, irrespective of the actual surface properties:

16-Black-and-grey-surfaces (2)

Physically, this corresponds to the characteristic of large surfaces that as they reflect energy, there is very little chance that energy will strike the smaller surfaces; most of the energy is reflected back to another part of the same large surface. After several partial absorptions most of the energy received is absorbed.

Gray Surfaces: The gray surface is a medium whose monochromatic emissivity (ελ) does not vary with wavelength. The monochromatic emissivity is defined as the ratio of the monochromatic emissive power of the body to monochromatic emissive power of a black body at same wave length and temperature.

ελ = Eλ / Eλ, b

But, we know the following.

16-Black-and-grey-surfaces (3)

16-Black-and-grey-surfaces (4)


16-Black-and-grey-surfaces (5)

Where: Eλ,b is the emissive power of a black body per unit wave length. If the gray body condition is imposed, that is, ελ = constant, so that: ε = ελ = constant


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