AbbesRefractometer

Name:-Mangaljit Singh Abhijit SanjeevEntry No:-2014PHA2208 Entry No:-2014PHA2202

M.Tech in Applied OpticsIndian Institute of Technology, Delhi

Aim:-

To find refractive index of the given liquid samples using Abbes refractometer.

Apparatus:-Abbes refractometer, temperature controller, light source, cotton and liquid samples.

Theory:-

The Abbe instrument is the most convenient and widely used refractometer, Fig:-1 shows a schematic diagram of its optical system. Fig:- 1Schematic diagram of optical system[1]

The sample is contained as a thin layer (~0.1mm) between two prisms. The upper prism is firmly mounted on a bearing that allows its rotation by means of the side arm shown in dotted lines. The lower prism is hinged to the upper to permit separation for cleaning and for introduction of the sample. The lower prism face is rough-ground: when light is reflected into the prism, this surface effectively becomes the source for an infinite number of rays that pass through the sample at all angles. The radiation is refracted at the interface of the sample and the smooth-ground face of the upper prism. After this it passes into the fixed telescope. Two Amici prisms that can be rotated with respect to another serve to collect the divergent critical angle rays of different colors into a single white beam that corresponds in path to that of the sodium D ray. The eyepiece of the telescope is provided with crosshairs: in making a measurement, the prism angle is changed until the light-dark interface just coincides with the crosshairs. The position of the prism is then established from the fixed scale. Thermosetting is accomplished by circulation of water through the jackets surrounding the prism.

Fig:-2Inside view of telescope[3]

The Abbe refractometer is very popular and owes its popularity to its convenience, its wide range (nD= 1.3 to 1.7), and to the minimal sample is needed. The accuracy of the instrument is about 0.0002.AprecisionAbbe refractometer is also available; in which the improvement in accuracy is obtained by replacing the compensator with a monochromatic source and by using larger and more precise prism mounts. The former provides a much sharper critical boundary, and the latter allows a more accurate determination of the prism position.

According to the law of refraction, n=sin(i)/sin(r), where i and r are the angles of incident and refracted ray, n is a constant called the index of refraction. From this equation, it is evident that when light is incident upon a transparent body, there will be a definite angle of refraction corresponding to every angle of incidence. If the refractive index of the body is greater than that of the medium outside, the angles of refraction will be smaller than these corresponding angles of incidence. But the upper limit of the angle of incidence is 90 degrees. There will be a corresponding upper limit for the angle of refraction which determines the largest angle, which any ray penetrating the body may make with the normal. This angle is the critical angle of refraction rc. Its value is obtained from the basic equation by substituting i=90 or sin(i)=1 where n=1/sin(rc.).Consequently a measurement of the critical angle of refraction gives immediate information concerning the index of refraction.

To an observer inside a medium of refractive index n, all rays incident upon the surface from above are confined, upon refraction, within a cone corresponding to the angles of refraction from zero up to the critical angle, as illustrated in fig. 2, no illumination exists from any direction whose angle with the normal is greater than this critical angle. Consequently the critical ray makes a boundary between a dark and a light area. This is more clearly illustrated in fig. 3.

Fig:-3Darkness obtained beyond critical angle

For monochromatic illumination this boundary will be a sharp line. For measurements of the critical angle as commonly made in the laboratory, the circle of fig:- 4, illustrates the appearance of the field of view of the observing telescope.

Fig:-4Field of view of the observing telescope

It is not possible as a rule, to make a direct measurement of rc. For the grazing incident ray, i=90,we have 1=(ng/nx)sin(r) and for the ray emerging from the glass into the air. One can show that:-

where is the refracting angle of the prism.For greater convenience of measurement the refractometer built on this principle are equipped with a calibrated scale. The Abbe refractometer measures refractive indices over the range of 1.3 to 1.7 and is provided with a practically linear scale which can be read to 0.001 and is accurate to 0.0002. The essential feature of this instrument lies in the use of a pair of so called Amici prism, two similar 45-degrees prisms of high refractive index. A drop of the liquid whose index is desired is placed upon the hypotenuse of one prism, and the hypotenuse of the other prism is placed upon that of the first, so that the two together from a cubical block of glass. A telescope focused for parallel light as shown in fig:- 5 will show the characteristic divided field.

Fig:-5Characteristic divided fieldThe index of the liquid is then read directly from the calibrated scale. The calibration is made for sodium light, but the instrument can also be used with daylight illumination. This is made possible by the introduction of a compensator consisting of two direct vision prism. They can be rotated in opposite directions at equal rates, and form together a system of variable dispersion. In this way, an amount of dispersion can be introduced to counteract that of the specimen under examination. The compensator carries a scale by means of which a measurement of the dispersion of the material under examination may be obtained. Amici Prism:-AnAmici prism, named for the astronomerGiovanni Amici, is a type of compounddispersiveprism used inspectrometers. The Amici prism consists of twotriangular prismsin contact, with the first typically being made from a medium-dispersioncrown glass, and the second a higher-dispersionflint glass. Light entering the first prism isrefractedat the first air-glass interface, refracted again at the interface between the two prisms, and then exits the second prism at near-normal incidence.

Fig:-6 An Amici prism [6]The prism angles and materials are chosen such that onewavelength(colour) of light, thecentre wavelength, exits the prism parallel to (but offset from) the entrance beam. The prism assembly is thus adirect-vision prism, and is commonly used as such in hand-heldspectroscopes. Other wavelengths are deflected at angles depending on the glassdispersionof the materials. Looking at a light source through the prism thus shows theoptical spectrumof the source.

Fig:-7 Acompact fluorescent lampseen through an Amici prism[6]The dispersive Amici prism should not be confused with the non-dispersiveAmici roof prism.AnAmici roof prism, named for its inventor, the ItalianastronomerGiovanni Amici, is a type of reflectingprismused to deviate a beam of light by 90 while simultaneously inverting the image. It is commonly used in the eyepieces oftelescopesas an image erecting system. It is sometimes called anAmici prismorright angle roof prism.The non-dispersive Amici roof prism should not be confused with the dispersiveAmici prism.The device is shaped like a standard right-angled prism with an additional "roof" section (consisting of two faces meeting at a 90 angle) on the longest side.Total internal reflection from the roof section flips the image laterally. Thehandednessof the image is unchanged.The roof faces of the prism are sometimescoatedto providemirrorsurfaces. This allows the prism to be constructed with other beam deviate angles besides 90 without being limited by total internal reflection

Fig:-8 An Amici roof prism[7]Now, in the measurements of the refractive index, light is directed into the prisms along the axis of the telescope by means of a mirror attached to the instrument. The eyepiece is focused simultaneously on the cross-hair and the scale by properly turning the eyepiece. Using sodium light, the adjustment for an index of refraction reading consists in turning the lower adjusting screw in such a way that a double field half bright half dark with a sharp dividing edge passing through the center of the cross-hair is seen. Then the index of refraction is read off the scale to the third decimal and the fourth decimal is conveniently estimated. When white light is used, the compensator must be adjusted before final adjustment of the prisms as described below in the procedure.If polychromatic radiation is used, no single sharp boundary such as that in fig:- 9 is observed. Instead, a diffuse chromatic region between the light and dark areas develops; the precise establishment of the critical angle is thus impossible. This difficulty is overcome in refractometers by the use of monochromatic radiation. As a convenient alternative, many critical angle refractometers are equipped with a compensator that allows the use of radiation from a tungsten source, but compensates for the resulting dispersion in such a manner as to give a refractive index in terms of the sodium D line. The compensator is made of Amici prisms, as shown in Fig:- 10. The properties of this complex prism are such that the dispersed radiation is converged to give a beam of light that travels in the path of yellow sodium D line.

Fig:-9

Fig:-10Amici prism for compensation of dispersion by sample. Note that yellow radiation (sodium D line) suffers no net deviation from passage through the prism.[1]

Temperature dependence of refractive index:-The refractive index of a liquid varies with density, primarily because the density of liquids varies with temperature. One can approximate the dependence with the equation:-

whereT0is some standard temperature where the index of refractionn(T0)is the known index of refraction n atT0, andTis the temperature coefficient of the index of refraction of the given liquid. Values ofTvary, but they tend to be 0.0003 to 0.0004 for liquids with n < 1.63 (all of the liquids in this lab) and approximately 0.0007 for liquids with n > 1.63. For simplicity, we takeTto be 0.0004.

Wavelength dependence of refractive index:-The refractive index of a material varies with wavelength, a phenomenon which is called chromatic dispersion. In the visible spectrum, it can be represented to a good approximation by Cauchys equation

Where A and B are constants that depend on the material, and is the vacuum wavelength. For example, at 20 C, for water A = 1.324 and B = 0.00319 m2; and for ethanol, A = 1.352 and B = 0.00318.

Procedure:-

General directions: The student is cautioned to handle the refractometer with extreme care.The prisms are made of flint glass; they are brittle and at the same time extremely soft. Therefore they are easily broken and scratched. Be sure to keep the surfaces of the prisms clean and to use only clean liquid on them.

1:-The scale and the cross-hair in the circle are focused by turning the eyepiece.

2:-To lift the upper prism off for applying the sample to be tested, turn the small knob attached to the prism into such a position, that the arrow mark at the side points upward; if it points sideward, the prism is locked in position. With the knob in the free position, swing the upper prism out into its rest position. By means of a smooth glass rod apply a drop of the liquid to be tested of the fixed prism and bring the upper prism back on top of the lower one.

4:-Start sodium light source and adjust its position, open the reflecting mirror of the upper prism and if necessary, adjust it for good illumination of the circle seen through the telescope; if necessary adjust the tube providing the illumination of the scale.

5:-Adjust the positions of the prisms by turning the knob at the lower right until in the middle of the bright circle a clear boundary line is observed between a dark gray sector in the lower half and a bright sector in the upper half of the circle. Make a fine adjustment of the prism position by turning the knob at the lower right until the boundary line passes through the center of the cross-hair.

6:-Read off the index of refraction on the illuminated scale directly up to the third decimal and estimate the value of fourth.

7:-Read and record the temperature of the thermometer attached to the instrument.

Repeat this procedure with other samples. Repeat one of the measurements using white light. This requires the operation of the built-in compensator. The compensator is adjusted by turning the knob at the middle of the instrument. Start with the compensator at the zero mark. Adjust the prisms gradually until a bright red-orange light appears across the middle of the circle. This will be the adjustment close to the final position. For further refinement turn the compensator knob until the color disappears and a sharp boundary line is obtained separation a gray sector in the lower part and a bright sector in the upper part of the circle opening. Read just the prisms until the boundary coincides with the center of the cross-hair. Read the value of the index of refraction and the thermometer as before and compare with the result of the previous measurement.

Trouble-shooting [2]

a. The viewing area does not show a separation into a light and a dark field.Check briefly if the range that you are in right now is anywhere +/- 0.05 units of the expected refractive index (literature value) if not, make sure to get close to this range by using the adjustment knob on the right side. Keep in mind that it is relatively sensitive.

b. The viewing area shows fancy colors and not just a light and a dark field.This is often observed if not enough material is applied to the prism and an uneven film is coating the prisms. The same effect is observed if the hinged prism is not pushed all the way down or the sample is inhomogeneous or strongly colored.c. There is not light in the viewing area.Is the instrument turned on? Is the lamp raised to its correct position?

Note:- Before every observation, clean the lower and upper amici prism surface thoroughly.

Sources of Errors:-[5]The secret to getting the most accurate possible refractometer readings is, in a word, "temperature." Even if a refractometer is automatically temperature compensated you will not get the most accurate results if you do not allow temperatures to equilibrate (equalize).Temperature is one of the single most important factors influencing accurate refractometer readings and is one of the largest sources of error in measurement. Refractive index is VERY dependent on temperature. The amount of error per degree of temperature is different for every fluid and differs for different concentrations of the same fluid. Although temperature compensation relieves the user of the responsibility to measure temperature and apply a correction factor when taking readings, it is not infallible.Whether you are using a traditional analog refractometer, a digital handheld refractometer, or a desktop refractometer, you must allow time for the refractometer temperature, the ambient temperature, and fluid temperature to come to equilibrium .Since the volume of fluid is usually only a few drops, its thermal mass compared to that of the refractometer is really rather small, allowing it to come to the temperature of the refractometer relatively quickly, in most cases. Thick viscous fluids, like maple syrup, typically take longer to come to equilibrium than less viscous material such as water.It will take a little time for a refractometer to adjust to changes in environmental temperature. For instance, if you take a refractometer from a cool air-conditioned laboratory out onto a shop floor on a hot summer day, it will take some time for the refractometer to equalize with the temperature in the shop. Likewise, if in the winter you are carrying a refractometer under a winter coat next to your body and then pull the refractometer out to make a measurement, it will naturally take some time for the refractometer to adjust to the change in ambient temperature.Everyone asks, How much time? There is no magic answer to this since there are too many variables. Each situation is different. But, providing the refractometer and ambient temperature are in equilibrium, as a general rule of thumb, you should wait about 10 seconds for every 5 F difference between refractometer temperature and 68F, or about 30 seconds for each 10 C difference between the fluid temperature and 20 C.How do you know if the temperature is stable? For the Palm Abbe digital handheld refractometer, if the rate of change of temperature exceeds a certain limit then the refractometer will not allow you to take a reading. However, it is possible that when putting a hot sample on a room-temperature refractometer the initial rate of change will be very high for the first 10 to 20 seconds and then level off and drift slowly towards equilibrium. If temperature is drifting relative to time you can expect to see some drift in your reading as well. So, if your refractometer readings are slowly drifting in one direction then there is a chance that the temperature is not stable. The direction of the drift depends on the nature of the changing temperature. Generally, if the temperature is stable and you take five measurements in a row, the readings should not vary by more than the precision of the scale.Another issue of concern is evaporation. Evaporation is vaporization that takes place at the surface of a liquid. The process of evaporation will increase the larger the surface area, the higher the liquid's temperature, the higher flow rate of air past the surface, and the lower its density. The Palm Abbe refractometer mitigates the effects of evaporation by limiting the fluid volume/surface area and inhibiting air flow with its Evaporation Cover. If a sample is rapidly evaporating, you can expect to see an upward drift in the refractometer reading over time.For the most accurate possible refractometer readings, take your time and allow the temperature of the refractometer, the ambient environment, and the fluid sample to come to equilibrium. As a general rule of thumb, you should wait about 10 seconds for every 5 F difference between refractometer temperature and 68F, or about 30 seconds for each 10 C difference between the fluid temperature and 20 C.Sample Calculations:-Least Count (L) =0.0005

S. NoName of SampleMain Scale Reading(say u)Small Division(say w)Refractive Indexn=u+L*w

1Watera1.33181.3390

b1.33171.3385

2Propan-2-ola1.3831.3815

b1.3811.3805

31-Bromonaphtalene

a1.65121.6560

b1.65101.6550

4Benzenea1.551.5025

b1.531.5015

5Non-Staining Oila1.4671.4635

b1.46101.4650

6Machine Oila1.4611.4605

b1.4621.4610

Mean value of refractive index of Water=1.33875Mean value of refractive index of Propan-2-ol =1.3810Mean value of refractive index of 1-Bromonaphtalene =1.6555Mean value of refractive index of Benzene =1.5020Mean value of refractive index of Non-Staining Oil =1.46425Mean value of refractive index of Machine Oil =1.46075References:-[1]:- http://amrita.vlab.co.in/?sub=1&brch=195&sim=545&cnt=1[2]:- http://www.chem.ucla.edu/~bacher/General/30BL/tips/refract.html[3]:- http://www.refractometer.pl/Abbe-refractometer[4]: http://www.mikroskop-online.de/Mikroskop%20BDA%20Gruppe%2032/32-110f-2%20%20Abbe%20Refractometer.pdf[5]:-http://www.misco.com/training/refractometer-general/47-the-secret-to-accurate-refractometer-readings[6]:- http://en.wikipedia.org/wiki/Amici_prism[7]:- http://en.wikipedia.org/wiki/Amici_roof_prism5