72 Immersion Lenses and New Refradometers. 



It would seem that these writers must be unacquainted with 

 the standard works on Optics, and so of course should not be ex- 

 pected to know that the angle of total internal reflexion or " critical 

 angle," as it is called, is dependent upon the refractive indices of 

 hoth media through which the incident ray is jpassing. Thus Dr, 

 Parkinson, F.E.S., in his edition of Eev. W. Grriffin's ' Optics ' : — 



" Definition. — The angle whose sine is — , which the angle of 



incidence in the denser medium must not exceed, in order that 

 refraction into a rarer medium may be possible, is called the critical 

 angle of the media between which the refractive index is p." 



To find the mutual index of refraction between glass and water, 



F' (0^ shorter ^a ) Y)v. Parkinson gives the following 



glass water \ g w/ '-' ^ 



example (p. 76, ' Optics ') : — 



3 4 



" Ex. — From air into glass ju = - : from air to water ix = — . Hence from 

 glass to water (denser to rarer medium) 



index from air to water 



G w index from air to glass 



^8"/ 4 3X 

 9 V 3 2/ 



in other words, the index of refraction for rays passing from water 

 9 . . 9 



into glass is ^ , and the critical angle is that whose sine is 1 -i- ^ 

 o o 



g 



or Q , i. e. 62^ 44'.* This nearly agrees with Ptolemy's 62°. 



The distinction between the critical angles when air is not one 

 of the refracting media is not given in general in popular works on 

 Optics, although so well described by Ptolemy. 



Professor Haughton writes (p. 28, ' Optics ') : — " The total 



* Ptolemy's value is 02"^. Taking these values we have from the ordinary 

 o 

 tables, since x = ■ 88889 nearly, 



log. 0-88889 = 1-94885 = log. sin. 62= 44', or 62° 44' instead of 62°. 

 g 

 The rough approximation - gives nearly the same result as the decimal values 



of fi in the two cases, viz. 1-500 and 1-336, usually employed when the value 



becomes 62° 57'. 



g 



Again, for 80° the sine of angle of refraction = - sin. 80° 



I X 0-9848078 = 0-8753847 = sin. 61° -5' 



The refractive index of the glass used by Ptolemy, since that for water is known, 

 was nearly that of plate or crown glass : as will be found by the formula 



sin. <(> 

 ~ sin. *' 



