H. R. CARLETON. 



XCIII. 



Prob. 6. 



SPHERICAL LENS. 



Let F be the source of light. 



Let P be a point on the outer curve, 



and FT, the horizontal axis of lens. 



a = the angle of incidence on outer curve. 



ft = the angle of refraction from outer curve. 



The inner curve is described from F as centre, with radius 

 depending on size of lantern. 



Required the equation to outer curve. 



B = 6 + a 



and sin (3 = //, sin a 



.'. fji sin a = sin (0 + a) ... ... ... (1) 



FPT = ^ = £ + a. 



. a = \p 



and from (1) ^ sin (if/ - r>) = sin ( 6 + if/ - « ) 

 . *. fi cos x// = cos (6 + if/) 



— cos 6 cos if/ - sin 6 sin if/ 

 .'./*,-= cos 6 - sin 6 tan if/ 



cos - fx 



tan i/r 



sin 6 



dB 

 But tan if/ = ry 



