[ 40 ] 



Y. Investigations in Optics, with special reference to the Spec- 

 troscope. By Lokd RayleigHj F.R.S. 



[Continued from vol. viii. p. 486.] 



§ 7. Aberration of Lenses and Prisms. 



THE following investigation refers to the aberration of 

 rays in the primary plane. Let Q be a radiant point 

 in air, from which rays fall Fig. 17. 



upon the spherical surface 

 of glass APB ; of radius r. 

 We require an approximate 

 expression for the length of 

 any ray Q P referred to that 

 of a standard ray Q A. 



POA = a), QAH = <^ 

 QA=m. PA = 2^sin(i&>). 

 QAP=i7r + </> + i&>. v 



QP 2 =z U 2 + 4r 2 sin 2 J co + Aru sin 1 co sin ((/> + \ co), 



so that as far as the cube of co, 



Qr — u = r sin (£ . co + - ( cos H r ) co 2 



rsin<ft /l [ r cos ft [ r 2 cos 2 cf> \^ ~. 



Similarly if Q x be any other point, and Q / A=w / ? Q / AH = ^> / , 

 Q'P-t*'=rsin ft' . ©+ | (cos ft' + !^*') *> 2 



^ sin ft' /l , r cos ft' r 2 cos 2 ft' \ , ( . 



If QP ; Q'P be incident and refracted rays corresponding to 

 g) = ^ the condition must be satisfied that 8(QP) = /aS(Q'P) 

 as co passes from the value 6 to 6 + S0. Thus 



(?* COS CD \ 

 COS ft -i -£ J 



_ sin ft /-, , 3r cos ft 3r 2 cos 2 ft\ ,, 2 

 2 \ w ^4 2 / 



• j./ i / ±r , ?*cos 2 ft'\ n 

 = fji sm ft' + /x ( cos ft' H j- 1 - J 6 



shift'/ 3?- cos ft' 3?' 2 cos 2 ft'\ , 2 . 



