Lambert’s‘cosine law

Lambert s cosine law Lambic beer Lamb modes Lambs Lamb wave Lamellae Lamepon Laminar flow Laminated fabrics Laminated glass... 

The intensities of diffuse reflectance and fluorescence are both distributed over the solid angle according to Lambert s cosine-law. An ultraviolet-visible (UV/VIS)-... 

The radiance observed from a body depends on the elevation angle 0, which is the angle from the surface normal at which the measurement is made. If 8 is independent of 0, the radiance at 6, is given by Lambert s cosine law ... 

Since the observer views radiation from all parts of the extended area A, but at different angles a, Lambert s cosine law, which states that the intensity in a given direction will change in proportion to the cosine of the angle from the normal, has to be taken into account.) Equ. (10.45a) is equivalent to... 

In radiative exchange calculations, it is preferable to use the model, described in the previous section, of a grey, diffuse radiating body as a simple approximation for the radiative behaviour of real bodies. As Lambert s cosine law is valid for this model, we denote these bodies as grey Lambert radiators. The energy radiated from them is distributed like that from a black body over the directions in... 

The blackbody spectral and total intensities are independent of direction so that emission of energy into a direction at 6 away from the surface normal direction is proportional to cos 6. This is known as Lambert s cosine law. 

Two main types of models for tubular lamps (the most widely used) will be described. There are lamps that produce an arc that emits radiation and, consequently, photons come out directly from such an arc. Emission is made by the whole lamp volume. We call this process Voluminal Emission. There are other types of lamps in which the discharged arc between electrodes induces an emission produced by some particular substance that has been coated on the lamp surface. We call this process Superficial Emission. Voluminal emission may be safely modeled as an isotropic emission in this case the specific intensity associated with each bundle of radiation originated in some element of volume of the lamp is independent of direction, and the associated emitted energy (per unit time and unit area) is also isotropic (Figure 6.6). On the other hand, it seems that superficial emission can be better modeled by a diffuse type of emission that is also known as one that follows the Lambert s cosine law of emission in this case the emitted intensity is independent of direction but the emitted energy depends on the surface orientation and follows the cosine law equation (Figure 6.7). The following assumptions are made (Irazoqui etal., 1973) ... 

The extinction coefficient depends on temperature, pressure, composition, and the wavelength of the incident radiation. It may be pointed out that Equation 19.9 is also termed as Lambert s law or Bougher-Lambert law, and Beer s law when the extinction coefficient is put in mass terms, but it must not be confused with Lambert s cosine law. 

Scattering is the opposite effect of regular reflection. If the surface is inhomogeneous by some micrometers within the irradiated area, one finds diffuse reflection [9]. Each area forms a center of reflection and the different reflected beams superimpose to result interference. The form of this intensity distribution within space can be described according to Lambert s cosine law. This effect is used in thin-layer chromatography [9,11]. 

Melamed developed an elegant mathematical description of absorption and scatter from an assembly of close packed spheres [64], Unfortunately, it is remembered more for its failings than its elegance. The Melamed model embodied two assumptions There would be reflection from the front external surface of a particle (that would follow Lambert s cosine law for a sphere), and there would be isotopic scatter from inside the particle. Within the sphere, the model took into account an infinite number of internal reflections. The model predicts that reflectance would reach a maximum as the relative refractive index approached zero. Of course, if there is no refractive index difference between that of the particle and the medium, there is no reflection from the particle. 

A light beam reflected from a difluse surface does not remain in the same plane, hut may be instead reflected omnidirectionally, i.e., in any spatial direction (e.g., [261]). Such behavior is ideally described by Lambert s cosine law. 

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