Nature and Optical Efficiency of the Mtrfors [Aft?I]> 



cased for taking notice of in this place, as altliongli devoid of noVelty 

 and interest to the scientific reader, they are nevertheless indispensable 

 to a proper understanding of what follows, by those who may have devo- 

 ted less of their time and attention to the subject. 



TVhen the rays of light proceeding from a luminous point are reflected 

 froiji a plane, they proceed after reflection in lines which will slope as 

 much from the plane as they before sloped towards it.— Namely, if A d, 

 A d' (Fig. 5) be any rays of light proceeding from a point A and strik- 

 ing a plane BC, they will after reflection slope /row the plane at angles 

 Bde, Bi^'e'— equal to the angles A C, A d' C at which they before 

 sloped towards it. Hence it may be easily deduced that the obliquity 

 of the rays d e, d' e' — from the front of the plane is exactly the same as 

 that of the lines d d' i' , in which they would have proceeded to the 

 rear of it if not intercepted. The effect of the reflection being exactly 

 the same as of the light at A were turned half round an imaginary axis 

 B C to a new position at F, so that the raj^s proceeded to the front in- 

 stead of the rear of plnie as shown in the figure. 



It must also be remarked, that the divergence of the rays w^ith respect 

 to one another remains unaltered, the angle e f e' being in every case un- 

 changed, and continuing equal to the angle i a i', the effect being merely 

 to reverse the wdiole of the rays composing the hemisjihere of light next 

 the plane, without in the least interfering with their relative inclinations. 



If we now suppose a plane polished surface to be placed immediately 

 in rear of the im.aginary sphere of light before spoken of, it will be easy 

 to imderstand from what has just been explained, that its effect w^ould be 

 to turn the whole* of the n.ys comprised in the rear hemisphere, and 

 Criuse them to proceed in directions exactly similar to those. pursued by 

 the rays emanating from the front one. In applying this to the aid of 

 Light-house illumination, therefore, such^a contrivance, would, in cases 

 vrhen only half of the circumference of the horizon is required to t 

 illurainated, double the useful light, by in fact converting one complete 

 sphere of luminous rays into two fro7it, instead of one front, and one 

 rear hemisphere. 



What has been hitherto said has referred only to a single luminous 

 point infinitely small, but as the same is equally true regarding every 

 point constituting a body of light of any size, it follows that in every 

 situation from which it has been shown that the rays from a single point 



* This of coarse supposes the plane to he unlimited in extent, as the rays nearest the 

 rliameter AD would not meet it, except at an infinite'distance. In practice, therefore, the 

 tp/inle of the rays cannot be returned by a plane mirror, for the same is true also when 

 taken in ^.lateral direction, and the number lost will depend upon the size of the plan^ 

 and its distance from the radiant point. 



