ANGLE REFRACTOMETRY 



and Arago is still valid. The original prism 

 of Arago and Biot was large, yielding directly 

 the absolute n value of gases or liquids rela- 

 tively to vacuum. 



The apex angle is conveniently made 143°. 

 (Instruments of this type are no longer com- 

 mercially a^'ailable.) The path of light is 

 first determined with the prism either evacu- 

 ated or filled with dry air. In a second opera- 

 tion, one measures with the specimen filling 

 the prism. 



Refractive Index Measurement with 

 the "Autocollimator."A small instrument 

 constructed especially for the measurement 

 of small angles or small defects of parallelism 

 in mechanical parts and machines, known as 

 the "Tuckerman Autocollimator"*, can also 

 be used for the measurement of the refrac- 

 tive index of transparent substances. 



The autocollimator consists essentially of 

 a highly corrected objective lens, in the focal 

 plane of which is a high-precision reticle. 

 Part of this reticle is illuminated to form a 

 fiduciary object. The parallel light emerging 

 from the lens can be reflected by anj^ external 

 plane surface back into the instrument, and 

 the reflected image can be made to fall on the 

 main scale of the reticle. 



The position of the reflected image of the 

 reticle is a function of the orientation of the 

 mirror, and this can be measured by means 

 of another scale in the fiducial image, which 

 acts as a vernier to the main scale of the 

 reticle. An eyepiece is provided to observe 

 the images. The distance from the mirror to 

 the instrument does not affect the readings, 

 so that the instrument can be used to meas- 

 ure the degree of parallelism between two 

 plates separated by a transparent medium. 

 If two such plates form a small angle a (un- 

 known), the interposed medium having a 

 refractive index n, the measured angle be- 

 ing d, one has: 



Conversely, if a and d are known, one 

 calculates n: 



n = sin d/s\n (2a) 



(S) 



The Goniometer. For the measurement 

 of small angles involved in a number of 

 methods mentioned herein, it is often con- 

 venient to use the goniometer. The goniome- 

 ter method is based upon a property of the 

 refracting prism already described, i.e., the 

 existence of a minimum deviation angle. The 

 determination of the refractive index 7i re- 

 quires measuring the minimum deviation 

 angle. This involves moving both the prism 

 and the telescope, as in the Biot and Arago 

 method. However, a greater accuracy is 

 possible with the goniometer by rotating the 

 prism on the turntable so as to give it suc- 

 cessively two exactly symmetrical positions. 



A modification of the method permits 

 measurements on liquids. Instead of a solid 

 prism, the goniometer is equipped with the 

 double rectangular liquid compartment of 

 Hallwachs. The table is oriented so that 

 light falls at grazing incidence on the plate 

 of glass separating the two fluids and one 

 observes the angular deviation relatively to 

 the direction of the rays when the two com- 

 partments are empty: 



sin- d = Hi 



2 _ 



n2 



(9) 



a = 



arc sin (sin d/n) 



(7)t 



* Mfd. by Aminco, Silver Spring, Md. 

 t (For equations 1-6 see next article). 



(?ii and n2 are indices of the fluids filling the 

 two compartments, respectively). By using a 

 double switching method and taking read- 

 ings in two opposed directions at 180°, dif- 

 ferences of refraction of the order of 1.5 X 

 10~^ can be measured. 



Other Methods of Angular Measure- 

 ments. A number of refractometric meth- 

 ods involving angular measurements to be 

 carried out with non-specialized instruments 

 have been developed primarily for the ana- 

 lytical chemist. The required implements are 

 usually a microscope, a goniometer, or a 

 simple type of photometer. 



Microscopic methods utilizing the Becke 

 lines displacement are described in textbooks 



487 



