R E F 



ami .*. as before 



I 



1 



Cor. If E be the centre of the mirror, Q and q the foci of incident and 

 reflected rays, F the principal focus of parallel rays, 



F?:FE::FE:FQ 



where Q and q lie on the same side of F, move in opposite directions, 

 and meet at the centre and surface of the reflector. 



III. Reflexion, images produced by. 



\. When an object is placed between two parallel plane mirrors, a row 

 of images is formed, which are gradually fainter as they are more re- 

 moto, and at length become invisible. 



Xow let A and B represent the two mirrors, O the object between 

 thazn, and let O' be the image of O at the mirror A, O" the image of O' 

 at the second mirror B, O'" the image of O" at the mirror A &c. 



Also let O be the image of O at the second mirror B, O the image of O 

 at A, O of O at B &c. and let it be required to find the distances O O 7 , 

 O O" , ........... OO,OO &c. 



Put O A a. O B = b, A B = c or a + b. Then 

 O O' 2 a X SO O 2b 



O O' 2 a X SO O 2b 



O O" - 2 c f J O O = 2c 



> Again < " 

 O O'" ~2c + 2a( JOO=2e 



2. Suppose now that the mirrors, instead of being parallel, are inclined 

 to each other, in this case the number of images will be limited, and will 

 evidently lie in the circumference of a circle, whose centre is the inter- 

 section of the two planes, and radius the distance of the object from that 

 intersection. 



Now let H I and K I be the mirrors, O the 

 object, then as before there will be two series 

 of images 



O', O", O'" &c. and O, O, O &c. 



to determine the distances O O', O O" &c. mea- 

 sured along the circumference of the circle, put 

 e I O or II O - 6, O I K or O K = fi', H I K 

 t or H K = ;, then 

 231 



