10 Mr. W. H, M. Christie on the [Mar. I, 



Simple Prism. 



Let 0, 0' be the angles of incidence and refraction. 



\p, \p' be the angles of emergence and refraction, $ and \p being con- 

 sidered positive when they fall on the side of the normal away 

 from the edge of the prism. 



/J. the refractive index. 



a the refracting angle of the prism. 



m the magnifying-power. 



A the dispersion. 



II= — the purity. 



m 



D the deviation. 

 Then 



sin0 = ^usin0', (1) 



sin — sin (2) 



+ f = a (3) 



and 



D = (j) + \p — a. 



1. Magnifying-power. 



Let ty= angle between two incident pencils. 



3^/= angle between the two corresponding emergent pencils. 



Then 



Magnifying-power m = — 



Now (1) and (2) give, fi being constant, 



cot <p c<p=cot </>'£</>', and cot \p Si// = cot ^'Si// ; 



and from (3) 



$0 Sty h(f>' 



m _ co * x Cot ^' — C0S ^ C0S ^' — -^ reac ^k °^ indent pencil 

 ~~ cot(f cot ^ cos ^' ' cos \p Breadth of emergent pencil' 



as will be seen at once by drawing perpendiculars to the incident, re- 

 fracted, and emergent pencils. Also, if 



, cot <t>' ,, cot -dJ 



m= — — m =—J., 

 COt (j) cot ^ 



. m" 

 we have wi= — 7 . 



m 



We may call m', m" the magnifying-powers of the first and second sur- 

 faces respectively, whence, 



.„ . f» i ie • Magnifying-power of second surface 



Maenifymg-power of half -prism =— =—2 — 4 r . 



^ r r Magnitymg-power 01 nrst surface 



