Anaya Nolan
The law of reflection, which states that the angle of incidence is equal to the angle of reflection, has been known in some form since at least 1021, when Alhazen described what would later be known as Snell's law in his Book of Optics. The law of reflection was further developed by Thomas Harriot in 1602, Dutch astronomer Willebrord Snellius in 1621, René Descartes in 1637, and Pierre de Fermat around 1660.
| Characteristics | Values |
|---|---|
| Creator of the law of reflection | Alhazen, Thomas Harriot, Willebrord Snellius, René Descartes, Pierre de Fermat, Christiaan Huygens, Nicolaas Bloembergen |
| Date of creation | Alhazen's Book of Optics was published in 1021, Thomas Harriot's work was in 1602, Snellius' work was in 1621, René Descartes' essay Dioptrique was in 1637, and Fermat's work was in 1660 |
| Other names for the law of reflection | Snell's law, la loi de Descartes, loi de Snell-Descartes, Huygens-Fresnel principle |
| Applications | Optics, electromagnetic theory, medical diagnosis, optical communications, sonar, seismology, radio transmission, radar |
| Laws of reflection | The angle of incidence equals the angle of reflection; the incident ray, reflected ray, and normal to the reflection surface lie in the same plane; the reflected ray is always in the plane defined by the incident ray and the normal to the surface at the point of contact |
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What You'll Learn
The law of reflection and refraction
The law of reflection states that the angle of incidence is equal to the angle of reflection when light reflects off a smooth surface. In other words, the angle at which the light ray hits the surface is the same as the angle at which it is reflected. This principle can be used to understand how mirrors produce images.
The law of reflection was discovered by a person from Alexandria, who noticed that the angle of incidence equals the angle of reflection. This person also realized that this law could be rephrased to state that reflected light travels along the shortest path or in the least amount of time, assuming it has a finite speed. Later, in around 1660, Pierre de Fermat generalized this idea to a least-time principle for all light rays.
Reflection is the change in direction of a wavefront at the boundary between two different media, causing the wavefront to return to the medium from which it came. This phenomenon is not limited to light; sound and water waves, for example, can also undergo reflection. Specular or regular reflection occurs when the reflecting surface is very smooth. On rough surfaces, diffuse reflection takes place, where light is reflected in many different directions.
Refraction is the bending of light rays as they pass from one medium to another, or as the characteristics of the medium through which they are travelling change. The law of refraction, also known as Snell's law, describes the relationship between the angle of incidence and the angle of refraction with respect to the normal line to the surface. It predicts the degree to which light will bend as it crosses the boundary between two media, which is determined by the difference in their refractive indices.
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Specular reflection
The laws of reflection for specular reflection are as follows:
- The incident ray, the reflected ray, and the normal to the reflection surface at the point of incidence lie in the same plane.
- The angle which the incident ray makes with the normal is equal to the angle which the reflected ray makes to the same normal.
- The reflected ray and the incident ray are on opposite sides of the normal.
The law of reflection states that the angle of incidence equals the angle of reflection. This was noticed by Euclid of Alexandria and later generalized by Pierre de Fermat around 1660, who introduced the idea that light takes the shortest path or time.
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The Fresnel equations
Fresnel's equations give the ratio of the reflected wave's electric field to the incident wave's electric field, as well as the ratio of the transmitted wave's electric field to the incident wave. These ratios are known as amplitude coefficients and are usually represented by the lower-case letters "r" and "t", respectively. The equations assume that the interface between the media is flat and that the media are homogeneous and isotropic. The incident light is assumed to be a plane wave, and there are two sets of Fresnel coefficients for the two different linear polarization components of the incident wave.
The s polarization refers to the polarization of a wave's electric field normal to the plane of incidence, while the p polarization refers to the electric field vector in the plane of incidence. In 1821, Fresnel derived results equivalent to his sine and tangent laws by modelling light waves as transverse elastic waves with vibrations perpendicular to the plane of polarization. He experimentally confirmed that his equations correctly predicted the direction of polarization of the reflected beam when the incident beam was polarized at 45 degrees to the plane of incidence.
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Total internal reflection
The critical angle depends on the refractive indices of the two media. For example, at a water-air surface, the critical angle is 48.5°. As the indices of refraction depend on wavelength, the critical angle will vary slightly with wavelength and colour. Below the critical angle, both refraction and reflection occur in varying proportions.
The phenomenon of total internal reflection has various applications. It is used in binoculars, periscopes, telescopes, and other optical instruments. It is also employed in fibre optics, where light rays are guided through long, twisting paths by multiple total internal reflections in glass or plastic fibres.
The law of reflection, formulated by Ibn al-Haytham (Alhazen) of Alexandria around 1021 AD, states that the angle of incidence equals the angle of reflection. This can also be understood as the reflected light taking the shortest path or time. Pierre de Fermat generalised this principle around 1660, introducing the concept that in a medium with a refractive index of μ, light travels more slowly than in free space by a factor of μ.
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The work of Pierre de Fermat
Pierre de Fermat was a French mathematician who made significant contributions to various fields of mathematics. He is often regarded as one of the greatest mathematicians in history. Born in Beaumont-de-Lomagne, France, in either late 1607 or early 1608, Fermat had a passion for mathematics from a young age. Fluent in six languages, Fermat was also praised for his written verse and his expertise in emending Greek texts.
Fermat is recognized for his original method of determining the greatest and smallest ordinates of curved lines, which laid the groundwork for differential calculus. He is also credited for his work in analytic geometry, where he demonstrated that an equation from algebra could be represented as a geometric curve. Fermat's work in this field was independent and simultaneous with that of René Descartes, and it earned him the title of founder of modern number theory.
In addition to his work in calculus and analytic geometry, Fermat made notable contributions to optics and the study of light refraction. He refined the understanding of the law of reflection by articulating the principle of least time, stating that "light travels between two given points along the path of the shortest time." This principle, now known as Fermat's principle, is a key concept in physics and optics.
Fermat also made significant contributions to probability theory, working alongside Blaise Pascal. Their collaboration resulted in advancements that laid the foundation for probability theory. Fermat is also remembered for Fermat's Last Theorem in number theory, a challenging problem that remained unsolved for over three centuries.
Despite his remarkable contributions, Fermat did not publish his work during his lifetime. Most of his mathematical insights were shared through correspondence with fellow mathematicians or discovered in his notes after his death. Fermat's work continues to be celebrated, and he is recognized as a guiding light in the invention of calculus and a pivotal figure in the development of fundamental principles in physics and mathematics.
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Frequently asked questions
The law of reflection was first discovered by Alhazen in 1021.
In his Book of Optics, Alhazen formulated the law of reflection, which states that the angle of incidence is equal to the angle of reflection.
The law of reflection is used to understand the images produced by plane and curved mirrors. It also has applications in acoustics, geology, and electromagnetism.
Yes, Thomas Harriot, Willebrord Snellius, René Descartes, and Pierre de Fermat all made significant contributions to the understanding and development of the law of reflection.
The law of reflection states that when light reflects off a smooth surface, the angle at which it reflects is the same as the angle at which it hits the surface.
