What is reflection?

It is the phenomenon by which a wave striking the separation surface (interface) between two different media does not cross the interface, but changes its direction of propagation, going back into the medium it came from. In general the incident wave is partly reflected and partly transmitted into the second medium (where it may be absorbed). To quantify the fraction of energy reflected, a pure number between zero and one is introduced, called the reflection coefficient, defined as the ratio between the reflected energy and the total incident energy.

In the following sections we illustrate

• which law relates the direction of incidence and the direction of reflection;
• what happens if the interface is small compared with the wavelength of the light;
• which physical factors determine the reflection efficiency of the interface.

The billiard law

${\displaystyle {\theta }_i=}$angle of incidence ${\displaystyle {\theta }_r=}$angle of reflection n=normal to the surface Billiard players know from experience that, in shots without spin, the angle of incidence is equal to the angle of reflection. In shots off several cushions, they are helped to predict the path of the ball by a series of markers (diamonds) on the cushion of the table which, empirically, make it possible to take this simple law into account. For physicists, the law so formulated is a consequence of two facts: the cushion pushes the ball only in the direction perpendicular to itself, so the component of the velocity parallel to the cushion does not change; and the collision is almost perfectly elastic, so the ball keeps its kinetic energy and the component of the velocity perpendicular to the cushion reverses direction without changing in size. This law must be completed by the observation that, in the case of reflection in space, and not in a simple plane like the billiard table, the incident ray, the normal to the interface and the reflected ray must lie in the same plane.

Specular reflection

In the corpuscular interpretation of light, the billiard law helps to predict in a simple way how mirrors work, that is, surfaces worked so as to "reflect" an incident light ray almost completely in a well-defined direction.

Plane mirror

In the case of the plane mirror, the interface is a plane. The figure alongside shows the working principle of a plane mirror based on the "billiard law". The observer's eye, used to considering that light travels in a straight line, when hit by the reflected ray assumes that the light comes from an object placed behind the mirror.

The explanation is so simple that for a long time it was one of the strong points of the corpuscular (Newtonian) interpretation of light. We are indeed fully within the domain of geometrical optics, since the size of the interface is much greater than the wavelength of the incident light (see wave ray and diffraction to look into the question further).

The wave interpretation explains reflection by means of Huygens' principle: the reflected wavefront ${\displaystyle A{S}_3}$ arises as the envelope of the secondary spherical waves generated by the points ${\displaystyle S_1}$, ${\displaystyle S_2}$, ${\displaystyle S_3}$ at the moment they are hit by the incident wave. Compared with the simple explanation provided by the "billiard law", it is Huygens' explanation that looks contrived! For simplicity, the figure shows a single wavefront of the reflected ray. Had we drawn more than one, we would have noticed that the "spacing" between two successive wavefronts (that is, the wavelength) would have turned out to be the same as that of the incident wavefronts. This is an obvious consequence of the fact that the propagation speed of the reflected ray is equal to that of the incident ray, since it depends only on the characteristics of the medium in which the wave phenomenon propagates. If you want to see an animation that clearly shows the equality between the angle of incidence and the angle of reflection the equality of the wavelength of the incident wave and of the reflected one, visit our 2D Waves virtual laboratory and carry out the experiment described on the page Reflection from a plane mirror

Parabolic mirrors and more

Parabolic mirrors (that is, those whose interface is shaped as a parabola or a paraboloid) have an extraordinary "focal" property that justifies their use on the roofs of our houses to receive the electromagnetic waves coming from the "satellite": rays parallel to the axis of symmetry of the mirror generate reflected rays all passing through the same point, called the focus. If a receiver is placed at the focus, it will be able to detect all the rays striking the parabolic mirror, with an obvious improvement in the quality of the received signal. The condition just described occurs if the "pointing" of the dish is optimal: the rays coming from the satellite, it is worth repeating, must be parallel to the axis of symmetry of the parabolic mirror. If the alignment is not optimal one speaks, not by chance, of an "out of focus" signal (no longer correctly collected at the focus).

The ability of parabolic mirrors to concentrate signals is, for geometrical optics, an immediate consequence of the focal properties of that very special curve called the parabola and of the "billiard law". To apply the latter, it must be specified, as for every "curved" mirror, that the angles of incidence and of reflection at a given point are measured with respect to the perpendicular to the tangent line to the curve at that point (see the figure alongside).

The explanation in wave terms, that is, using Huygens' principle, is so complicated (it already was for the plane mirror!) that it is better, once again, to visit our 2D Waves virtual laboratory and carry out the experiment described on the page Reflection from a parabolic mirror

Reflection from grids

When we think of a mirror, we think of a smooth, extremely compact surface able to reflect very efficiently the waves that strike it. It is surprising to discover that reflection can also occur if the reflecting surface is a mesh, like chicken wire: the surprise obviously comes from the fact that the surface appears to be full of holes which, at first sight, should let the wave through instead of reflecting it. In reality, if the wavelength of the incident wave is much larger than the size of the holes, the surface behaves as a mirror.

This principle is exploited, for example:

• in the cooking cavities of microwave ovens;
• in the receiving apparatus of radio telescopes, which can in fact be made of metal grids;

Diffuse reflection

Most objects do not behave like a mirror but, when they receive an incident light ray, they reflect it more or less in all directions. This phenomenon is called diffuse reflection and plays a role in the fact that we can also see non-luminous objects, that is, objects that do not emit light radiation by themselves. Our eyes are hit by the radiation scattered by bodies. The spectral composition of the scattered radiation determines the colour of bodies. One criterion for establishing whether a given interface will reflect specularly lies in the "roughness" of the surface: if the average depth of the surface irregularities is much smaller than the wavelength of the incident light, the reflection will be specular. It is interesting to note that this is a relative criterion, in the sense that a surface that reflects a wave of a certain wavelength specularly may reflect a wave of a different wavelength diffusely.

The example always given is that of the bottom of an iron pan: it reflects microwaves (of long wavelength) specularly, but not visible light (of shorter wavelength). The practical effect of all this is that you cannot see your reflection in the bottom of a pan!!.

How much is reflected?

The fraction of energy reflected depends on how different the two media are, and precisely on their impedance, the quantity that measures how much a medium "opposes" the motion produced by the wave. If the two media have the same impedance the wave passes without being reflected; the more different the impedances, the more the wave is reflected. For example, the acoustic impedance of water is about 3600 times that of air: a sound arriving from the air on the surface of a lake has 99.9% of its energy reflected. This is why someone under water hears very little of the noises coming from outside. The same happens to a wave travelling along a string made of two pieces of different thickness (see reflection on strings, refraction in one dimension (in Italian) and transmission and reflection coefficients).

Does every body reflect?

From what has been said, it seems that every body must reflect, either specularly or diffusely. But what happens if the transverse dimensions of the reflecting interface become comparable to (or smaller than) the wavelength of the incident wave? To find out by experiment, we invite you to visit our 2D Waves virtual laboratory. Below we propose a series of guided experiments, but you are free to try new configurations and new experiments. The app is very intuitive; to understand correctly what you observe, just keep in mind that the coloured areas represent the amplitude of the oscillation. The brighter the colour, the larger the amplitude of the oscillations (green for crests, red for troughs).

• Diffraction by an obstacle

The experiment leaves little doubt: when the size of the obstacle is smaller than the wavelength of the incident wave, the obstacle is not able to reflect the incident wave significantly. Instead of being reflected, the wave continues almost undisturbed, as if it had not "seen" the body!

This is only one of the possible cases of the typical wave phenomenon called diffraction.

The following table gives the typical wavelengths of some waves and the characteristic sizes of some obstacles.

Try using the table to answer the first two questions in the section Check your understanding.

Check your understanding

Further reading and links

• Visit the page on diffraction to look further into the subject
• Reflection plays a fundamental role in the formation of standing waves in strings and in the "tubes" of musical instruments. If you want to look further into the subject, visit the sections Reflection in strings and interference between reflected waves.
• Reflection is of course not limited to light waves, but concerns every kind of wave. In the particular case of sound waves it is responsible for the well-known phenomenon of echo and plays a fundamental role in determining the acoustics of a room.