R E F 



3. In a circular arc, whose tangent is t, 



For rectification of Spirals see Spiral. 

 REFLEXION in Optics. ( Coddington. ) 

 1. Reflexion at plane surfaces. 



1. To find the direction in which a ray of light, emanating from a 

 given point, takes after reflexion at a plane mirror. 



Let the ray proceed from a point Q, and a perpendicular Q C be drawn 

 to the surface of the reflector, and let the ray after reflexion cut Q C 

 produced in q ; then will Q and q be on opposite sides of C, and Q C will 

 -Cq. 



2. To find the same when the ray is reflected alternately by two plane 

 mirrors inclined to each other at any given angle. 



Let if be the / of incidence at the first reflexion 



I. second 



i the inclination of the two mirrors j then we shall have this series 

 of equations, 



(n 1) t 

 * n 



or <p <p (n 1) ; 

 n i 



If now $ be any multiple of /, as (n 1) /, we shall have somewhere? 



= 0, i.e. some reflected ray will be perpendicular to one of the mirrors, 

 n 



and these of course will end the series of reflexions. If $ be not a mul- 

 tiple of ;, some value of n will make (n 1) i greater than <p, and then <p 



' n 



will be negative. This shews that the ray will at length be turned back 

 upon itself in a direction contrary to what it at first proceeded in. 

 To find the angle between the 1st incident and last reflected ray, let 

 229 N3 



