Keith Mack
Snell's Law, also known as the Law of Refraction, is an equation that relates the angle of the incident light and the angle of the transmitted light at the interface of two different mediums. It can be applied to all materials, in all phases of matter. The law states that the ratio of the sine of the angles of incidence and transmission is equal to the ratio of the refractive index of the materials at the interface. When light travels from one medium to another, it generally bends or refracts, and the degree of refraction depends on the refractive indices of the media through which the light rays are travelling.
| Characteristics | Values |
|---|---|
| What is it? | An equation that relates the angle of the incident light and the angle of the transmitted light at the interface of two different mediums. |
| When is it used? | When light or other waves pass through a boundary between two different isotropic media, such as water, glass, or air. |
| What does it state? | The ratio of the sines of the angle of incidence and the angle of refraction is equal to the refractive index of the second medium with respect to the first. |
| What is the formula? | \({\displaystyle {\frac {\sin \theta _{1}}{\sin \theta _{2}}}=n_{21}={\frac {n_{2}}{n_{1}}}={\frac {v_{1}}{v_{2}}}}\) |
| How is it derived? | From Fermat's principle, Huygens's principle, Maxwell's equations, or conservation of energy and momentum. |
What You'll Learn
The law of refraction
When light travels from one medium to another, it generally bends or refracts. The law of refraction allows us to predict the amount of bend. This law is more complex than the law for reflection, but an understanding of refraction is necessary for our future discussion of lenses and their applications.
${\displaystyle {\frac {\sin \theta _{1}}{\sin \theta _{2}}}=n_{21}={\frac {n_{2}}{n_{1}}}}$
Where θ1 is the angle of incidence, θ2 is the angle of refraction, n1 is the refractive index of the first medium, and n2 is the refractive index of the second medium.
The refractive index of a material is defined as:
${\displaystyle n={\frac {c}{v}}}$
Where c is the speed of light in a vacuum and v is the speed of light in the material.
As light passes the border between two media, depending on the relative refractive indices of the two media, the light will either refract to a lesser angle or a greater one. These angles are measured with respect to the normal line, represented perpendicular to the boundary. If the second medium has a higher refractive index than the first, the light will be refracted towards the normal line as it slows down. Conversely, if the second medium has a lower refractive index, the light will be refracted away from the normal line.
Snell's Law can be applied to all materials, in all phases of matter. It is especially important for optical devices such as fiber optics.
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Refractive indices
The refractive index of a material is defined as the ratio of the speed of light in a vacuum to the speed of light in that material. The refractive index can also be determined from the permittivity and permeability of the material. The index of refraction is always greater than or equal to one because light travels at a slower speed in a material than in a vacuum. The refractive index of air is approximately 1, while the refractive index of water is approximately 1.333.
When light passes through different media, it generally bends or refracts. The amount of bend can be predicted using Snell's Law and the refractive indices of the materials involved. If the second medium has a higher refractive index than the first, the light will be refracted towards the normal line, as it is slowed down. Conversely, if the second medium has a lower refractive index, the light will be refracted away from the normal line.
Snell's Law can be applied to all materials, regardless of their state of matter. It is particularly important in the design of optical devices such as lenses and fiber optics. By understanding Snell's Law and the refractive indices of different materials, engineers can create more effective optical devices.
Additionally, Snell's Law can be used to explain various optical phenomena, such as the apparent shortening of legs when standing in water or the brilliance of diamonds due to their high refractive index.
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How light changes speed
Light travels at different speeds depending on the medium through which it passes. In a vacuum, light travels at a constant speed of 299,792,458 metres per second (approximately 300,000 kilometres per second). This speed is often referred to as 'c' and is used as a standard unit of measurement.
However, when light passes through transparent media such as air, water or glass, its speed decreases. This reduction in speed is described by the refractive index of the medium, which is always greater than one. The refractive index of a material is calculated by dividing the speed of light in a vacuum (c) by the speed of light in that material. For example, glass has a refractive index of around 1.5, so light will pass through it at a speed of c/1.5, or approximately 0.7c.
The change in speed of light as it passes through different media can be described by Snell's Law, which relates the path taken by a ray of light as it crosses the boundary between two substances with different refractive indices. This law states that the ratio of the sines of the angle of incidence and the angle of refraction is equal to the refractive index of the second medium with respect to the first.
Snell's Law can be applied to all materials, in all phases of matter. It is particularly important in the design of optical devices such as fibre optics, where it is used to guide light along fibres that are not laid out in straight lines.
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How light changes direction
Light can change direction when it passes through a boundary between two different media, such as water, glass, or air. This phenomenon is known as refraction, and it is described by a formula called Snell's law.
Snell's law states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the refractive indices of the two media. In other words, it relates the path taken by a ray of light as it crosses the boundary between two substances to their refractive indices. The refractive index of a medium represents how much the speed of light decreases when passing through that medium compared to a vacuum.
As light passes through the border between two media, its direction will change depending on the relative refractive indices of the substances. If the refractive index of the second medium is higher than that of the first, the light will be refracted toward the normal line—an imaginary line perpendicular to the boundary. Conversely, if the refractive index of the second medium is lower, the light will be refracted away from the normal line.
For example, when light travels from air into water, it is refracted toward the normal line because water has a higher refractive index than air. This is due to the decrease in the speed of light as it passes through water compared to air. On the other hand, light travelling from water to air would refract away from the normal line.
Snell's law is essential for understanding and designing optical devices such as fibre optics. It also explains why objects may appear shortened when partially submerged in water—the light rays are bent as they pass from the water back into the air, changing the direction in which they enter our eyes.
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Total internal reflection
For example, when looking at a fish tank from below, the water-to-air surface reflects the underwater scene like a mirror with no loss of brightness. This is because the light rays are totally internally reflected back into the water.
The critical angle is the smallest angle of incidence that yields total reflection, or the largest angle for which a refracted ray exists. When the angle of incidence is greater than the critical angle, the sine of the angle of refraction is greater than one, which is impossible. Therefore, the light is completely reflected back into the original medium.
The critical angle can be calculated using the formula:
> θc = sin^-1 (n2 / n1)
Where n1 is the refractive index of the first medium, and n2 is the refractive index of the second medium.
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Frequently asked questions
Snell's Law, also known as the Law of Refraction, is a formula that relates the angle of incident light to the angle of transmitted light when it passes through a boundary between two different media.
Snell's Law states that the ratio of the sines of the angles of incidence and transmission is equal to the ratio of the refractive indices of the two media.
The refractive index is a number that is constant for a given medium and is related to the speed of light in that medium.
If light is passing through the same medium, the refractive indices will be the same, and the ratio of their values will be 1. This means that the sines of the angles of incidence and transmission will also be equal, indicating that light will continue in a straight line with no refraction.
