# Reflection

## Table of contents

Reflection is the change in direction (rebounding) of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Most objects are visible because of the light that reflects from them.

The reflection of a body in motion is a particular case of impact. In the study of reflection of elastic and electromagnetic waves it is convenient to introduce the concept of ray to simplify the geometric constructions necessary to determine the laws. The rays identify the direction of propagation of the wave and at each point are perpendicular to the wave surface. Defining angle of incidence and angle of reflection respectively the angles formed by the incident ray and the reflected ray with the normal at the point of incidence, the laws of reflection, valid for all wave phenomena, are: the incident ray, the reflected ray and the normal at the point of incidence lie in the same plane; the angle of incidence is equal to the angle of reflection.

The phenomenon of reflection is often accompanied by that of refraction and absorption. The reflection laws can be obtained by applying Huygens’ principle, according to wave theories.

The reflection laws are valid if the dimensions of the surface of separation of the two media are much greater than the wavelength of the incident light; otherwise diffraction phenomena occur. In most cases, the reflected wave does not have all the energy of the incident wave, because a part is transmitted to the next medium, in relation to both the more or less specular character (then the mechanical finish) of the separation surface, and the physical characteristics of the two media. It is called reflection factor the ratio ρ between the energy of the reflected wave and the energy of the incident wave.

When the separation surface of the two media is irregular, the energy of the reflected wave is distributed among several directions around a central direction, and the reflection is called diffuse reflection or diffusion. Total reflection is a reflection phenomenon that occurs under appropriate conditions (see refraction).

## Types and characteristics

The adjectives are used to indicate the type of reflection involved:

• spectral to indicate monochromatic radiation, i.e., considered wavelength by wavelength;
• radiant (as opposed to luminous) to indicate that the radiation is given in terms of total energy, that is expressed by radiometric quantities;
• luminous (as opposed to radiant) to indicate that the radiation is weighted according to the luminous efficiency function of the eye, that is expressed in photometric quantities.

Reflection can occur:

• specularly (specular or regular reflection) i.e. in a single (or almost) direction
• diffusely (diffuse reflection) that is in various directions.

The reflectance is the ratio between reflected flux and incident flux evaluated for each wavelength. Being defined as a ratio of homogeneous quantities, reflectance is a dimensionless quantity and is expressed as a percentage (0-100%) or as a factor (0.0-1.0). It also concerns the flux and therefore the totality of the radiation reflected in the hemisphere. The artificial material with the lowest reflectance is Vantablack.

## Reflectance factor

Reflectance is not only a function of wavelength but also of illumination, radiation geometry, and viewing geometry (i.e., the geometry by which the body is illuminated and the geometry by which the reflected amount is measured), so it is necessary to define a more general quantity of reflectance, namely the reflection factor.

Reference is made to the ideal reflecting diffuser. This is a body (ideal, i.e. theoretical) that does not absorb or transmit, but diffusely reflects the received radiation with equal radiance or luminance for each angle of reflection and regardless of the direction of incident radiation. As a first application of the concept of ideal reflecting diffuser, the radiance factor or luminance factor is defined as the ratio between the radiance of an area and that of the ideal reflecting diffuser radiated in the same way.

With reference to this ideal body, the reflectance factor or reflection factor of a body is the ratio between the flux reflected by the body in a given cone whose vertex is on the body considered and the flux reflected by the ideal reflecting diffuser.

The reflection factor is therefore a generic quantity that corresponds:

• to the spectral reflectance if the cone is a hemisphere;
• to the spectral radiance factor if the cone is narrow.

A typical spectrophotometer can measure the spectral reflectance factor at 10 nm intervals in the range of 380 to 730 nm.

## Reflection in acoustics

The reflection of sound waves is of particular interest in problems of environmental acoustics (echo, reverberation time) and problems of acoustic insulation; in fact, the insulation given by a wall is largely due to reflection and in the remaining part to attenuation of sound energy inside the wall. In practical cases reflection is always accompanied by refraction and absorption; diffraction phenomena are very important in relation to the size of the obstacles.

## Reflection in telecommunications

The reflection of radio waves is part of the propagation mode of these waves in the atmosphere; in particular it occurs by reirradiation from a conducting surface and takes place by capture of the incident radio wave with transformation into an electrical signal at high frequency that, in turn, involves the emission of a new radio wave of lower intensity than the incident one, due to the losses that occur in the conducting medium at the time of capture and subsequent irradiation.

The reflection of radio waves follows the laws of optics and is of great importance, especially in the case of radio communications with metric and microwave waves, allowing the overcoming of natural and artificial obstacles along the path of radio waves. In order for good reflection conditions to occur, it is necessary that the reflecting surface has a size significantly greater than the wavelength of the incident radio wave. For this reason radars operate with radio waves of a wavelength of the order of a few centimeters.

Reflection in transmission lines occurs when the working impedance varies, both along the path and at the terminations, with respect to the value of the characteristic impedance of the line. The reflected waves, composing themselves along the line with the incoming signals, give rise to the formation of standing waves that, in addition to hindering the transmission of signals, cause significant losses in the conductors and the dielectric of the transmission lines. For this reason, efforts are made to reduce the causes of reflection.

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