Refractive Index

Table of contents

• Acknowledgments
• Theory
  • Refractive Index
  • Measurement of n_D
• Instrument
  • Abbé Refractometer
    • Procedure for Abbé Refractometer

Theory

Refractive Index

refractive index, n

the ratio of the sine of the angle of incidence of a ray of light in vacuum, (r) to the sine of the angle of refraction in the medium (m), which is equal to the ratio of the wave velocity of light in vacuum to the wave velocity in the medium.

The angles are measured relative to the normal of the interface between the two media.

For convenience sake, one usually uses air (at 1 atm) as the reference medium, instead of vacuum. The index referred to vacuum can be calculated from that referred to air by multiplying the value by the refractive index of air (1.00027).
By definition, the index of refraction of vacuum is 1.

The refractive index is a physical property of the medium that depends on the wavelength of the light, and the temperature. The wavelength used is that of the yellow sodium D line (a doublet 589.0-589.6 nm), and the index of refraction is given the symbol n_D.

The temperature needs to be specified, and is usually 20 or 25 degree Celsius. The refractive index decreases with increasing temperature, and for most organic compounds one can correct for the temperature using

The temperature at which the index of refraction is determined is usually included in the symbol as the superscript, e.g., n_D²⁰.

Measurement of n_D

The measurement of the refractive index is based on the determination of the critical angle of reflection.

critical angle

The incident angle at which the angle of refraction is 90^o.

Any ray in the medium with an angle of incidence larger than the critical angle will be totally reflected (at the same angle as the angle of incidence).

Instrument

The Abbé Refractometer for Liquids

One commercially available instrument for this measurement is the Abbé refractometer. It operates by determining the critical angle of reflection at the boundary of the liquid with a glass prism of known refractive index.
It has the advantages that

• a white-light source may be used, but the reading will be that for the sodium D line
• only a few drops of the liquid are required
• allows for temperature control of prisms and sample
• compensating Amici prisms allow one to determine the specific dispersion

The nature of the Amici prisms means that one can compensate for the wavelength dependence of the refractive index (specific dispersion). When white light is used the critical angles for the components of the light will be slightly different. Unless compensated for, this will give rise to chromatized rays around the average critical angle (giving the image in the viewer the colors of the rainbow).

Abbé refractometer

Procedure

1. To introduce the sample unlock the prism, lift the top prism, spread a few drops of the sample on the bottom prism, close the prisms slowly, and lock the prisms again.

   
   a 680kB QuickTime movie

2. Turn the instrument on (on/off switch).
   
3. Focus the eyepiece on the scale by rotating it.
   
4. Turn the scale adjustment so that the critical ray boundary is visible in the top part of the viewer (a dividing line between light and dark halves is visible).
   
5. Turn the Amici prism adjustment so as to achromatize the boundary.

    

   

   The center image shows proper achromatization (white color - sharp boundary).
   

6. Turn the scale adjustment so that the boundary between light and dark coincides with the center of the cross hairs.

   

7. Read and record the refractive index on the top scale in the lower part of the viewer (the bottom scale is for the concentration of sugar in water; ignore it). Three decimal places can be read, the fourth place is estimated.

   

   the image above shows a reading of 1.3433 (notice the smallest division is 0.0005).

8. If the specific dispersion is required, read and record the Amici prism adjustment knob.
   
9. Read and record the temperature on the thermometer.
   
10. Clean the prisms by opening them and wiping them clean (top and bottom). Use water to remove water soluble compounds, toluene or petroleum ether for water insoluble compounds. Be sure not to scratch the prisms.

    
    a 1MB QuickTime movie

11. Leave the prisms in an open position so they can air dry.
    
12. To compare the refractive index with a reported literature value determined at a different temperature, the temperature correction factor may be used.

    

    For a measured refractive index of 1.2821 at 18 ^oC, the reported value of the refractive index for this particular measurement should be n_D¹⁸ = 1.2812.

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