1892.] MICROSCOPICAL JOURNAL. 227 



equally well used when the beam travels in the opposite direc- 

 tion. 



Critical Angle. 



Whenever abeam of light passes into a denser medium, no 

 matter what the angle of incidence may be. there always corre- 

 sponds to it a certain angle of refraction ; such is not the case 

 wdien a beam passes from a denser to a less dense medium. 



Example: The beams SO, S'O, S"0 (figure 2) passing into a 

 denser medium are refracted at OR, OR', OR". A beam mak- 

 ing an angle of 90° with the normal would be refracted at OL. 



Reciprocally the beams OR, OR', OR'' in passing from a 

 dense into a less dense medium will give rise to the beams OS, 

 OS', OS '. The beam OL gives rise to the emergent beam OB, 

 which makes an angle of 90° with the normal. The angle of the 

 incident beam LO is the critical angle ; it is not refracted by 

 passing into the medium of lesser density, but is totally reflected. 



This angle may be determined for different media by an appli- 

 cation of the formula for obtaining the refractive index, as fol- 

 lows : 



Let the angle sought be called X. 



Refractive index = Ref. Lid. 



Ref. Ind.^ ^'"" 90° o, 

 sine X 



c- ,^ sine 90° I 



Sine X = ^— = 



Ref Ind. Ref. Lid. 



(One being the sine of an angle of 90°.) 



This (critical) angle for water is 48° 35' ; for glass, 41". 



The instruments used in tiie determination of refractive indices 

 are numerous. Some are quite simple and easy of use, while 

 others sue more complicated, and greater care has to be exercised 

 in manipulation. One of the most simple, and one that has given 

 satisfaction in my hands, is Bertrand's Refractometer (shown 

 at figure 4). It can be used for solids and liquids and gives the 

 index correct to two decimal places. By the use of monochro- 

 matic sodium flame one may obtain results correct to 3 or 4 deci- 

 mal places by a single reading. 



Description of instrument : AB is the eye-piece carrying a lens 

 of crown-glass of four centimetres' focus. It slides in the tube 

 CD, which is conical at the further end, and is provided with a 

 reticule, R, consisting of a glass disc 8 mm. in diameter, engraved 

 with So divisions y,^ mm. apart, and numbered by tens. CD 

 slides in the tube EFFH, the lower face of which is an elliptical 

 section making an angle of 30° with the axis, and carrying the 

 hemispherical flint-glass lens L of5 mm. radius fixed in a copper 

 disc. 



The plane surface of this lens faces outward and its centre is 

 in the axis of the instrument. FF is a small aperture filled with 



