Refractive Index Formula Overview
The refractive index is the ratio of the speed of light in a medium to the speed of light in a vacuum. When light travels in a medium other than a vacuum, the atoms of that medium absorb and re-emit light particles, reducing the speed of light.
What exactly is the Refractive Index?
The refractive index is defined as the ratio of light's speed in a vacuum to its speed in a certain medium and is often referred to as the refraction index or index of refraction. The speed of light in a medium is determined by the medium's qualities.
The speed of electromagnetic waves is determined by the optical density of the medium. The tendency of atoms in a substance to recover absorbed electromagnetic energy is referred to as optical density. The slower the speed of light, the more optically dense the substance. The refractive index is one such measure of a medium's optical density. The refractive index, commonly known as the index of refraction, is a measurement of the bending of a light beam as it passes through one material and into another. The refractive index n is defined as the ratio of the sine of the angle of incidence to the sine of the angle of refraction; n = sin I / sin r. The velocity of light c of a particular wavelength in empty space divided by its velocity v in a material, or n = c/v, is called the refractive index.
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Refractive Index And Colors
All colors have identical velocities in a vacuum. Their velocity varies as they go from a vacuum to another medium. As a result, colors have varying refractive indices. Colors' refractive indices change as their wavelengths change. Because violet has the highest refractive index, it travels the slowest and lies near the bottom of the rainbow. Red, on the other hand, has the lowest refractive index and hence goes the fastest and is at the top.
Refractive Index Formula
The refractive index has no dimensions. It is a number that represents how much slower a light wave would be in the substance than in a vacuum. The refractive index, denoted by the symbol n, is the ratio of the velocity of light in a vacuum to the velocity of light in a medium.
n = c/v
where,
n = refractive Index
c = speed of light
v = phase velocity of light
The refractive index of the vacuum is one. The above equation may be used to compute the refractive index of different materials. The greater the refractive index, the larger the optical density and the slower the light speed.
The table below includes the refractive index of different mediums.
|
Materials |
Refractive Index |
|
Ethyl Alcohol |
1.36 |
|
Ice |
1.31 |
|
Water |
1.333 |
|
Air |
1.0003 |
|
Diamond |
2.417 |
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Optical polymers have a High Refractive Index
High refractive index optical polymers allow light rays to bend more within the material, decreasing the lens profile. Furthermore, when the refractive index rises, the thickness of the lens falls, resulting in reduced weight.
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Refractive Index Influencing Factors
The refractive index is also impacted by temperature and light wavelength-
|
Factors |
Description |
|
Light Wavelength |
Because different wavelengths interact with atoms of a material to varying degrees, the refractive index changes linearly with wavelength. Monochromatic lighting should be used to avoid light dispersing into multiple hues. The medium should not absorb the given wavelength. |
|
Temperature |
The refractive index is typically determined at room temperature. A greater temperature causes a liquid to become less thick and viscous, allowing light to move quicker in that medium. As a result of the decreased ratio, the refractive index has a lower refractive index value. A lower temperature causes a liquid to become denser and more viscous, forcing light to move more slowly. As a result of the higher ratio, the refractive index value is higher. |
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Example of a Refractive Index
The refractive index of glass is 1.52, while that of water is 1.33. Because glass has a greater refractive index than water, the speed of light in water is quicker than the speed of light through glass. When the refractive index of one medium exceeds that of another, the first medium is said to be optically denser. The majority of the compounds we know have a positive refractive index with a value greater than zero. When a material possesses negative permittivity and permeability, it has a negative refractive index. The refractive index measures the relative speed of light in various mediums. Knowing the refractive indices of various media allows the learner to determine the direction in which light bends while traveling from one medium to another.
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Types of Refractive Index
There are primarily two types of refractive index, which are as follows-
|
Types |
Description |
Formulas |
|
Relative Refractive Index |
The Relative Refractive Index is the ratio of the velocity of light in one medium to the velocity of light in another and is the relative shift in the speed of light when it travels from one medium to another. If we have two distinct media, A and B. The refractive index will be as follows: Refractive Index of Medium B = Refractive index of Medium B in comparison to Medium A. |
nBA = Light Velocity in Medium A / Light Velocity in Medium B Similarly, nAB = Light Velocity in Medium B / Light Velocity in Medium A |
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Absolute Refractive Index |
The refractive index in a vacuum is called the Absolute Refractive Index. It is defined as the ratio of the velocity of light in a vacuum to the velocity of light in another medium. |
n = c/v, where c is the vacuum speed of light and v is the medium speed of light. |
Snell's Law- Angle of Refraction Calculation
When light travels from one medium to another, the refractive index influences how much its path changes. This angle of refraction is explained by Snell's law. Snell's law is sometimes referred to as the "Law of Refraction" and the "Snell-Descartes" Law. In 1621, Willebrord Snell discovered Snell's Law.
When light strikes a barrier between two media, it is partially refracted and partially reflected. Snell's law describes the relationship between the angle of incidence and the angle of refraction as light flows from one medium to another, such as air, glass, or water. The phase velocity ratio in two distinct mediums is equal to the ratio of the sine of the angle of incidence and the sine of the angle of refraction. Furthermore, it is the same as the refraction index ratio.
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Refraction Index Applications
Light refraction may be seen in numerous locations throughout our daily lives. It alters the perspective of objects below the surface of the water, making them look closer than they are. It serves as the foundation for optical lenses, which allow equipment such as glasses, cameras, binoculars, microscopes, and the human eye to function.
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Practical Applications of the Refraction Law
Optical tools include spectacles, lenses, and other devices. The following details are as follows-
- Camera Lenses: Knowing how much light will modify its course from a camera lens is desirable. This aids in the adjustment of the object's location.
- Contact Lenses: As a wearable lens, contact lenses must also be adjusted to each individual's eyesight.
- Liquids: Specific equipment is used to calculate refraction in liquids. This is used in industries when combining two liquids or for making particular types of candy.
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Refractive Index Gradient
The rate of change of the refractive index with respect to distance in the material is defined as the refractive index gradient. The slope of the refractive index profile at any location is referred to as the distance. The gradient of the refractive index is represented in terms of the reciprocal of a unit of distance. A refractive index gradient is the rate of change of the refractive index with respect to distance at any point in time. The gradient of the refractive index is a vector point function.
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Things to Keep in Mind
The following are the points to remember-
- The rate of change of the refractive index with respect to distance in the material is defined as the refractive index gradient.
- The frequency of the light wave is constant in all media.
- The refractive index changes as the wavelength changes.
- The ratio of the speed of light in a vacuum to the speed of light in any particular material is known as the refractive index.
- The speed of light in water exceeds that of light in glass.