XCII. 



NEW SOUTH WALES LIGHTHOUSES. 



Prob. 5. 



PLANO-CONVEX LENS. 



ProLJern 5 



Let F be the source of light. 



P, a point on curve. 



FT, the horizontal axis of lens. 



€ = angle of refraction at plane surface. 



90° - $ = angle of refraction at curved surface, 



<£ being angle of inclination of tangent at P to horizontal, 



APB = RPH = 90°-<£ 



APS = e 



.-. SPB = 90°-<£-e 



and sin RPH = /x sin SPB 



i.e., sin (90° - <j>) = /x sin (90° - - e) 



or, cos cf> = /jl cos (<£ -1- e) ... ... ... (1) 



Also sin 6 = /jl sin e ... ... ... ... (2) 



From (1) : cos <j> = /jl cos <£ cos e - [x sin cj> sin e and substituting 

 from (2) 



COS = fJL COS (f> 



Jl 



sin 2 6 



— sin cj> sin 



cos </> = cos <£ yf fx* - sin 2 6 - sin <j> sin 



1 = tA/A 2 - sin 2 - sin 6 tan 



tan <£ _^V 



6 





