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Refractive Index Theory

What is a refractive index?

The refractive index is a ratio of the speed of light in a medium relative to its speed in a vacuum. This change in speed from one medium to another is what causes light rays to bend. This is because as light travels through another medium other than a vacuum, the atoms of that medium constantly absorb and reemit the particles of light, slowing down the speed light travels at. The refractive index ( ) can be calculated using the equation below.

equation to calculate the refractive index

However, it is also important to note that light changes direction when it travels from one medium to another. Therefore, another method to calculate the refractive index of a medium is to apply Snell’s law, which will be very important later in our discussion of refractometers.

snells law

The refractive index of any other medium is defined relative to the refractive index of a vacuum, which is assigned a value of 1. Thus, a refractive index of 1.33 for water means that light travels 1.33 times faster in a vacuum than in water.

diagram showing refraction of light

Figure 1: The refraction of light. In this diagram, light travels faster in medium A than it does in medium B.

Refractive indices can be measured for different types of mediums including transparent or coloured solutions, turbid suspensions, emulsions, fine powders, ect.

Factors that affect the refractive index:

The two factors which affect the value of the refractive index are:
  1. Temperature
    • Refractive index values are usually determined at standard temperature.
    • A higher temperature means the liquid becomes less dense and less viscous, causing light to travel faster in the medium. This results in a smaller value for the refractive index due to a smaller ratio.
    • A lower temperature means the liquid becomes denser and has a higher viscosity, causing light to travel slower in the medium. This results in a larger value for the refractive index due to a larger ratio.
    • Refractometers usually have a means of temperature regulation.
  2. Wavelength of light
    • The refractive index varies with wavelength linearly because different wavelengths interfere to different extents with the atoms of the medium.
    • It is important to use monochromatic light to prevent dispersion of light into different colours.
    • The chosen wavelength should not be absorbed by the medium.
    • The sodium D line at 598 nm is the most frequently used wavelength of light for a refractometer.
Note: These two factors are present in the equation above,
where t = temperature in ºC and D = the wavelength of the light used in nm.

How is a refractive index measured?

A refractometer is used to measure the refractive index of a medium. There are many different types of refractometers, including the Abbe refractometer, which will be discussed in further detail below. A refractometer works based on the principle that light bends when it enters a different medium. This instrument measures the angle of refraction of light rays passing through the unknown sample. This measurement combined with the knowledge of the refractive index of the medium directly in contact with the unknown sample, are used to determine the refractive index of the unknown sample by applying Snell’s law described above.

The following cross sectional diagram illustrates the inner-workings of a refractometer. A light source shines on the illuminating prism and light rays enter the sample moving in different directions. The largest angle of incidence produced by a light ray (θi) produces the largest possible angle of refraction (θB). The other light rays entering the refracting prism all have a smaller refraction angle and lie to the left of point C. A detector at the back of the refracting prism produces the light and dark regions. In an Abbe refractometer, a detector is not present and there is more optics but the general scheme remains the same. Samples with different refractive indexes produce different angles of refraction which will cause a shift in the borderline between the light and dark regions. The borderline’s position is then used to establish the refractive index of different samples.

diagram showing cross of the octical path

Figure 2: A cross-sectional diagram of part of the optical path of an Abbe refractometer. The sample thickness has been exaggerated for clarity.

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