H. R. CARLETON. LXXXVII. 



The optical axis is the line in which a ray of light passes un- 

 changed in direction through a lens, and the principal focus is 

 the point from whence rays of light proceeding in a divergent 

 course are so changed by refraction at the inner and outer sur- 

 faces of a lens that they emerge parallel to the optical axis. 

 The position of the principal focus in a piano convex lens is 



r 



found by the formula F = r, in which r = the radius of 



J u — 1 



curvature of the lens, and //, the index of refraction, or it can be 



found by exposing the lens to the sun. As spherical lenses only 



parallelise those rays which are incident near the axis, this has 



led to the building of lighthouse lenses in separate pieces 



The Diagram shows a vertical section through the focus of a 

 first order dioptric fixed light. 



The focal distance determines the order of light. The focal 

 distance of a first order light is 36 '2 2 inches : the width of the 

 central disc is 1 1 inches : the annular rings which surround the 

 disc vary in width from 2 J to 1J inches, and are so arranged 

 that the lenses shall be as nearly as possible uniform in thickness, 

 and thus equalise the absorption. They are 20 in number, 

 placed half above and half below the central disc. Below these 

 zones are six triangular rings of glass ranged in cylindrical form, 

 and above are thirteen rings diminishing in diameter as they 

 recede from the optic axis, thus forming a dome which completes 

 the apparatus. 



Three or four problems in lighthouse optics will embrace suffi- 

 cient of the subject to enable us to trace the path of a ray in any 

 part of the apparatus before it leaves the lighthouse. The 

 approximate solution of these problems, in which the curves are 

 assumed to be circular arcs are given in Fresnel's work on light- 

 houses, and have been taken from that book, but the author also 

 submits what he believes to be a rigid solution in the case of 

 the path of a ray through the upper and lower triangular prisms, 

 in which the issuing rays of light are twice refracted and once 

 reflected. Fresnel, in dealing with the approximate solution of 

 this problem, assumes that the refracting sides of the triangular 



