Experiment 2 Index of refraction of an unknown liquid --- Abbe Refractometer

Transcription

1 Experient Index of refraction of an unknown liquid --- Abbe Refractoeter Principle: The value n ay be written in the for sin ( δ +θ ) n =. θ sin This relation provides us with one or the standard ethods of deterining the index of refraction of a substance, when it is in the for of a pris. By use of a spectroeter the anglesθ and δ ay be easured with great accuracy. Part : The pris angle θ Let the pris be placed on the spectroscope table as shown in figure, the edge of the pris towards the colliator, light falling upon and being reflected fro both surfaces. The telescope M is turned until light reflected fro face AB enters it, and an iage of the slit is seen by reflection in the field of view coinciding with the cross-hair. Now the telescope is turned into position M, so that an iage of the slit is seen by reflection fro AC. The difference is twice the angle of the pris. This is an illustration of the principle that if a plane reflector is turned through any angle, the reflected ray is turned through twice that angle. Part : The angle of iniu deviation δ The light ray will be refracted as it passes fro air into the pris and will proceed along the line MN. The angle δ in figure represents the total deviation of the ray resulting fro its passage through the pris. Fro figure we see the following relations:

2 α = φ + θ = 90 φ + θ β = 90 φ δ = 80 (90 φ ) (90 φ + θ ) = φ + φ θ When δ is a iniu, its derivative with respect to φ is zero. Hence, dδ = dφ dφ dφ + = 0 = dφ = dφ φ = φ dφ dφ Therefore angle δ is a iniu when the bea passed through the pris syetrically. In your report derive the equation for the index of refraction sin n = ( δ +θ ) θ sin( ) Procedure: Since this experient requires highly accurate work it is necessary to have the spectroeter in coplete adjustent. ) Focus the eyepiece on the cross-hair of the telescope. Direct the telescope toward the light, ove the eyepiece tube until the cross-hair are ost distinctly observed. Light rays fro the cross-hair which enter the eye are than parallel rays. ) Level the spectroeter. Place a level on the spectroeter plate, adjust the foot screws, turn the level on the plate, adjust again till the spectroeter is absolutely horizontal. 3) Level the spectroeter table. Place a level on the table so that it is parallel to a line through two of the leveling screws, and level by adjusting these screws. Then place the level at right to its first position, and level by adjusting the third screw. 4) Level the telescope and colliator. Place the level on top of the barrel of the telescope, and adjust by use of the leveling screw. In a siilar anner adjust the colliator. 5) Adjust slit of the colliator. Rotate the telescope until it is directly opposite the colliator and in alignent with it. Slide the slit assebly in the colliator tube until it is in sharp focus and without parallax with respect to the cross-hair. Reeber: Do not touch the eyepiece of the telescope. It has been focused for parallel light. 6) Put the pris on the pris table. The pris table should be leveled such that if the light through the hole in the Gaussian eyepiece, the two reflected iages on the cross-hair fro the two reflecting faces are both at the sae height as the cross-hair. 7) Measure the pris angle θ. Turn the pris table so that light can be reflected fro both faces siultaneously. Record the positions at which these reflections are seen in the

3 telescope. Be able to show that the difference between these two readings in θ. 8) Rotate the pris and the telescope to observe the deviated ray. Turn the pris table until iniu deviation is observed and record the readings. Then reove the pris fro the table and turn the telescope to observe the straight-through or un-deviated ray. Record the scale-readings. The difference between this set of readings and the readings of the light deviation is δ, the angle of iniu deviation. Proble: Calculate the index of refraction of the liquid fro the forula and deterine what liquid you used. n = sin ( δ +θ ) θ sin Apparatus: Spectroeter, ercury arc, hollow-pris filled with an unknown liquid, level. Proposed copositions: a) Water e) Carbon disulphide b) Benzene f) Carbon tetrachloride c) Nitrobenzene g) Toluene d) Ethyl alcohol h) Aniline Useful hints: Principle of Abbe refractoeter is described as following. The Abbe refractoeter is one of the ost accurate and ost convenient instruents for deterining the index of refraction. The easureent is based on the observation of the refracted bea passing through the substance to be easured and entering a standard pris of high refracting index at grazing incidence. 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. Fro 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 ediu outside, the angles of refraction will be saller than these corresponding angles of incidence. But the upper liit of the angle of incidence is 90 degrees. There will be a corresponding upper liit for the angle of refraction which deterines the largest angle

4 which any ray penetrating the body ay ake with the noral. This angle is the critical angle of refraction r c. Its value is obtained fro the basic equation by substituting i=90 or sin(i)= where n=/sin( r c )...() Consequently a easureent of the critical angle of refraction gives iediate inforation concerning the index of refraction. To an observer at 0, inside a ediu of refractive index n, all rays incident upon the surface fro above are confined, upon refraction, within a cone corresponding to the angles of refraction fro zero up to the critical angle, as illustrated in fig., no illuination exists fro any direction whose angle with the noral is greater than this critical angle. Consequently the critical ray akes a boundary between a dark and a light area. This is ore clearly illustrated in fig.. For onochroatic illuination this boundary will be a sharp line. For easureents of the critical angle as coonly ade in the laboratory, the circle of fig., illustrates the appearance of the field of view of the observing telescope. Since it is not possible as a rule, to ake a direct easureent of r c, equation () can not be directly applied to the deterination of indices of refraction. Moreover, since this ethod is coonly used to easure the index of refraction of a liquid by placing it in contact with a pris, it is of advantage to derive an expressing to take the place of equation () upon the assuption that the incident bea, upon passing into the pris, passes fro a ediu of index n x into the glass of index n g. Under these circustances, for the grazing incident ray, i=90 (ray c in fig. ) we have =( n g / n x )sin(r) and for the ray eerging fro the glass into the air (ray c). In addition r+r =Λ, where Λ is the refracting angle of the pris. By eliination of r and r fro these equations we finally obtain n = sin Λ n sin i' cosλsini'. x g

5 This equation expresses the index of refraction n of the ediu in contact with the pris for the condition of grazing incidence (ray c) of the light. For greater convenience of easureent the refractoeter built on this principle are equipped with a calibrated scale. The Abbe refractoeter easures refractive indices of solids and liquids over the range of.3 to.7 and is provided with a practically linear scale which can be read to 0.00 and is accurate to The essential feather of this instruent lies in the used of a pair of so called Abbe pris, two siilar 45-degrees= priss of high refractive index. A drop of the liquid whose index is desired is placed upon the hypotenuse of one pris, and the hypotenuse of the other pris is placed upon that of the first, so that the two together fro a cubical block of glass. It is then evident that for slightly convergent or divergent light incident fro an appropriate direction upon the junction of the two pris, a pair will be transitted and a part totally reflected if the index of the liquid is less than that of the priss. A telescope focused for parallel light as shown in fig. 3 will show the characteristic divided field. The index of the liquid is then read directly fro the calibrated scale. The calibration is ade for sodiu light, but the instruent can also be used with daylight illuination. This is ade possible by the introduction of a copensator consisting of two direct vision pris. They can be rotated in opposite directions at equal rates, and for together a syste of variable dispersion. In this way, an aount of dispersion can be introduced to counteract that of the specien under exaination. The copensator carries a scale by eans of which a easureent of the dispersion of the aterial under exaination ay be obtained. The ter dispersion in this case eans the difference in diffracting index for the wavelength of 6563 angstro (red), and 486 angstro (blue), respectively. Tables are supplied fro which this difference ay be obtained fro the copensator reading. In the easureents of the refractive index, light is directed into the priss and along the axis of the telescope by eans of a irror attached to the instruent. The eyepiece is focused siultaneously on the cross-hair and the scale by properly turning the eyepiece. Using sodiu light, the adjustent 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 decial and the fourth decial is conveniently estiated. When white light is used, the copensator ust be adjusted before

6 final adjustent of the priss as described below in the procedure. Procedure: General directions: The student is cautioned to handle the refractoeter with extree care. The priss are ade of flint glass; they are brittle and at the sae tie extreely soft. Therefore they are easily broken and scratched. Be sure to keep the surfaces of the priss clean and to use only clean liquid on the. ) The scale and the cross-hair in the circle are focused by turning the eyepiece. ) The illuination of the scale is adjusted by turning the sall tube projecting at the lower end of the instruent. 3) To lift the upper pris off for applying the saple to be tested, turn the sall knob attached to the pris into such a position, that the arrow ark at the side points upward; if it points sideward, the pris is locked in position. With the knob in the free position, swing the upper pris out into its rest position. 4) By eans of a sooth glass rod apply a drop of the liquid to be tested of the fixed pris and bring the upper pris back on top of the lower one. 5) Start a sodiu burner and adjust its position, open the reflecting irror of the upper pris and if necessary, adjust it for good illuination of the circle seen through the telescope; if necessary adjust the tube providing the illuination of the scale. 6) Adjust the positions of the priss by turning the knob at the lower right until in the iddle 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 adjustent of the pris position by turning the knob at the lower right until the boundary line passes through the center of the cross-hair. 7) Read off the index of refraction on the illuinated scale directly up to the third decial and estiate the value of fourth. 8) Read and record the teperature of the theroeter attached to the instruent. Repeat this procedure with other saples. Repeat one of the easureents using white light. This requires the operation of the built-in copensator. The copensator is adjusted by turning the knob at the iddle of the instruent. Start with the copensator at the zero ark. Adjust the priss gradually until a bright red-orange light appears across the iddle of the circle. This will be the adjustent close to the final position. For further refineent turn the copensator 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 priss until the boundary coincides with the center of the cross-hair. Read the value of the index of refraction and the theroeter as before and copare with the result of the

7 previous easureent. Finally, copare your results with the values given in tables.