REF 



00' -20 X /-OO-20' 



O O" = 2 < f J O O = 2 * 



. Again ^ 



O O" = 2 



and the number of images in the first series is the least whole number 

 greater than *""" ; and the number of images in the other series is 

 the least whole number greater than **'"" . 



If i be a measure of ar, the whole number of images is ; and in this 

 case two images of the different series coincide. 



3. If the object placed before a spherical reflector be a circular arc con- 

 centric with it, the image will also be a circular arc concentric with and 

 similar to the object, and its position and magnitude may be determined 

 by the proportion 



F 9 : FE :: FE : FQ. 



4. If the object placedbefore a spherical reflector be a straight line, the 

 image is a conic section ; and is a parabola, ellipse, or hyperbola, ac- 

 cording as the distance of the object from the centre of the mirror is 

 equal to, greater, or less than, half its radius. 



REFRACTION in Optics. (Coddington.) 

 I. Refraction at plane surfaces. 



1. Given the direction in which a ray falls on a plane surface bounding 

 a refracting medium ; to find the direction of the refracted ray. 



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

 drawn to the surface of the refracting medium, and let the ray after re- 

 fraction cut Q C or Q C produced in q ; put A and A' = C Q and Cq ; 6 

 and 6' ^'s. of incidence and refraction ; in the ratio of the sine of inci- 

 dence : sine of refraction, usually called the ratio of refraction , then 



t>r when 6 is small, as it is usually supposed to be, 



A' m A nearly. 



2. Let a ray pass through a refracting substance bounded by two 

 parallel plane surfaces ; to determine its direction after emergence. 



