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Snell's law, also known as the Snell–Descartes law, the ibn-Sahl law, and the law of refraction, was formulated by the Dutch astronomer and mathematician Willebrord Snell in 1621. Snell's law is a formula that describes the relationship between the angles of incidence and refraction when light or other waves pass through a boundary between two different isotropic media, such as water, glass, or air. The law is used in optics to compute the angles of incidence or refraction and to determine the refractive index of a material.
| Characteristics | Values |
|---|---|
| Who created Snell's Law | Willebrord Snell (also known as Snellius) |
| Year of discovery | 1621 |
| Field | Dutch astronomer and mathematician |
| Other names for Snell's Law | The Law of Refraction, Snell–Descartes law, ibn-Sahl law |
| What it describes | The relationship between the angles of incidence and refraction when light or other waves pass through a boundary between two different isotropic media, such as water, glass, or air |
| What it is used for | Determining the direction of light rays through refractive media with varying indices of refraction, computing the angles of incidence or refraction in ray tracing, and finding the refractive index of a material in experimental optics |
| Importance | Particularly important for optical technologies like fibre optics |
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What You'll Learn
The law was first discovered by Ibn Sahl in 984
The law, also known as the Snell-Descartes law, the ibn-Sahl law, and the law of refraction, was first discovered by Ibn Sahl in 984. Ibn Sahl was a Persian mathematician and physicist of the Islamic Golden Age, associated with the Buyid and Abbasid courts of Baghdad.
In 984, Ibn Sahl wrote an optical treatise, which was reconstructed by Roshdi Rashed from two manuscripts: Damascus, al-Zahiriyya MS 4871, 3 fols, and Tehran, Milli MS 867, 51 fols. The text of the treatise has the title "On Burning Instruments" or "The Book of Burners". In this work, Ibn Sahl dealt with the optical properties of
Ibn Sahl showed that it was not the angles but the sine of the angles that were linearly related. This means that the ratio of the sines of the angle of incidence is equal to the refractive index of the second medium with regard to the first. In other words, the law describes the relationship between the angles of incidence and refraction when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.
Using Snell's law, Ibn Sahl was able to derive lens shapes that focus light with no geometric aberrations, known as anaclastic lenses. He also dealt with parabolic mirrors, ellipsoidal mirrors, biconvex lenses, and techniques for drawing hyperbolic arcs.
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Willebrord Snell rediscovered the law in 1621
Willebrord Snell, a Dutch astronomer and mathematician, rediscovered the law of refraction, also known as Snell's law, in 1621. This law is fundamental to modern geometrical optics and is used to determine the direction of light rays as they pass through refractive media with varying indices of refraction.
Snell's law describes the relationship between the angles of incidence and refraction when light or other waves pass through a boundary between two different isotropic media, such as water, glass, or air. It is expressed as:
> n1/n2 = sin α2/sin α1
Where n1 and n2 represent the indices of refraction for the two media, and α1 and α2 are the angles of incidence and refraction that the ray makes with the normal line at the boundary.
Although the law was eventually named after Snell, it was originally discovered by the Persian scientist Ibn Sahl in 984. In his manuscript "On Burning Mirrors and Lenses," Sahl utilised the law to derive lens shapes that could focus light without geometric aberration. Despite this, Snell is credited with rediscovering the law in 1621, deriving a mathematically equivalent form that, unfortunately, remained unpublished during his lifetime.
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Snell's law is used to determine the direction of light rays
Snell's law, also known as the Snell-Descartes law, the ibn-Sahl law, and the law of refraction, is a formula used to determine the direction of light rays as they pass through different refractive media. It describes the relationship between the angles of incidence and refraction when light or other waves pass through a boundary between two different isotropic media, such as water, glass, or air.
The law was first discovered by the Persian scientist Ibn Sahl in Baghdad in 984. In his manuscript "On Burning Mirrors and Lenses," Sahl used the law to derive lens shapes that could focus light without geometric aberration. However, the law was eventually named after Snell, a Dutch astronomer and mathematician who independently rediscovered it in 1621.
According to Snell's law, the ratio of the sines of the angles of incidence and refraction is equal to the refractive index of the second medium concerning the first. Mathematically, this can be represented as n1/n2 = sin α2/sin α1, where n1 and n2 are the refractive indices of the two media, and α1 and α2 are the angles of incidence and refraction, respectively.
This law is particularly useful in optics, where it is employed in ray tracing to compute the angles of incidence and refraction. It also helps determine the refractive index of a material in experimental optics. For example, consider a ray of light moving from water to air with an angle of incidence of 50°. Using Snell's law, we can calculate the relationship between the angles of incidence and refraction, given that the refractive indices of water and air are approximately 1.333 and 1, respectively.
It's important to note that Snell's law is generally applicable to isotropic or specular media, such as glass. In anisotropic media, like certain crystals, the refracted ray may split into two rays, with only one of them following Snell's law. Additionally, the angles determined by Snell's law depend on the frequency or wavelength of light, causing a ray of mixed wavelengths to spread or disperse.
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The law is also known as the law of refraction
Snell's law, also known as the Snell–Descartes law, the ibn-Sahl law, and the law of refraction, is a formula that describes the relationship between the angles of incidence and refraction when light or other waves pass through a boundary between two different isotropic media, such as water, glass, or air. The law was discovered in 1621 by the Dutch astronomer and mathematician Willebrord Snell (also called Snellius). However, it is important to note that the law was first discovered by the Persian scientist Ibn Sahl in Baghdad in 984. In his manuscript "On Burning Mirrors and Lenses," Sahl utilised the law to derive lens shapes that could focus light without geometric aberration.
Snell's law is defined as "The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for the light of a given colour and for the given pair of media." This law is particularly useful in optics, where it is used in ray tracing to compute the angles of incidence or refraction and to determine the refractive index of a material. The refractive index of a material is the factor by which a light ray's speed decreases when travelling through that material compared to its velocity in a vacuum.
The law of refraction is also applied in the candy-making industry and is essential for optical devices such as eyeglasses, contact lenses, cameras, and fiber optics. In the case of fiber optics, Snell's law is crucial to understanding the phenomenon of total internal reflection, which is utilised for various applications, including telecommunications and data transmission in high-speed servers.
Furthermore, Snell's law can be derived from Fermat's principle, which states that light travels the path that takes the least time. This principle helps explain why light is refracted when it crosses the boundary between two different materials. The degree of refraction depends on the relative refractive indices of the materials, with the light bending towards the normal when entering a substance with a higher refractive index and away from the normal when entering a substance with a lower refractive index.
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It is generally true only for isotropic or specular media
Snell's law, discovered in 1621 by the Dutch astronomer and mathematician Willebrord Snell, describes the relationship between the path taken by a ray of light when crossing the boundary between two contacting substances and the refractive index of each. It is also known as the Snell–Descartes law, the ibn-Sahl law, and the law of refraction.
The law is generally true only for isotropic or specular media, such as glass, water, or air. An isotropic medium is one in which the permittivity and permeability of the medium are uniform in all directions. In other words, it exhibits uniformity in all orientations. This means that the index of refraction, or the phase velocity of a wave, is the same regardless of direction.
In contrast, materials are typically optically anisotropic, with different refractive indices in different directions. When light enters an optically anisotropic medium, it is resolved into waves with different properties and speeds. This can result in birefringence, where the refracted ray is split into two rays: the ordinary or o-ray, and the extraordinary or e-ray. The o-ray follows Snell's law, while the e-ray may not be co-planar with the incident ray.
Snell's law is used in optics to compute the angles of incidence or refraction and to determine the refractive index of a material. It is also applied to determine the direction of light rays through refractive media with varying indices of refraction.
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Frequently asked questions
Willebrord Snell (also known as Snellius) was a Dutch astronomer and mathematician.
Snell created Snell's Law in 1621, although it went unpublished during his lifetime.
Snell's Law (also known as the Law of Refraction) is a formula that describes the relationship between the angles of incidence and refraction when light passes through a boundary between two different media.
Snell derived Snell's Law using heuristic momentum conservation arguments in terms of sines.
Although Snell discovered the Law of Refraction, it was first discovered by the Persian scientist Ibn Sahl in 984. René Descartes also independently derived the law in 1637.
