KEAL AND VIRTUAL IMAGES. 



335 



Fig. 181. Real Image formed by 

 Concave Mirror. 



(fig. 181). Conversely, if held further from the mirror than the 

 centre of curvature, a real inverted but diminished image is 

 formed between the centre of curvature C and the focus F, AB 

 and ab in fig. 181 now changing places. In either case the image 

 can be received on a screen, magic lantern fashion; thus, if a 

 piece of greased letter paper be moved about in front of the mirror 

 together with a candle, numerous pairs of positions for the two 

 can be found, such that a distinct image of the candle appears on 

 the screen ; the relative positions 

 of candle and image for each pair 

 are said to be " conjugate " with 

 respect to one another; and the 

 term " conjugate foci " is applied 

 to represent the relative positions 

 of any two given points similarly 

 related to one another. The geo- 

 metrical focus of a concave mirror 

 has its conjugate focus at an in- 

 finitely great distance in front ; 

 that of a convex mirror at an 

 infinite distance behind; whilst 

 in all cases the relative positions 

 of any pair of conjugate points is expressed by a simple algebraic 

 formula depending on the focal length of the mirror.* 



It results from this, that a mirror with a surface of varying 

 radius of curvature will give a varying degree of magnification 

 or diminution; accordingly, by employing such mirrors, most 

 amusingly distorted reflections can be obtained according to the 

 curvatures of the surface. A vertical cylindrical mirror will not 

 distort at all in a vertical line, but will reflect as a plane mirror 

 would do arranged tangentially to the cylindrical surface ; in refer- 

 ence to a horizontal line, on the other hand, it will behave precisely 

 as a convex or concave mirror of the same radius of curvature. 



* If x be the distance from the mirror of one point serving as object, y 

 that of the other point or image, and/ that of the focus from the mirror, 

 then 



l + l -= 1 -, 



* y f 



the values of y and / being reckoned as + when measured in the same 

 direction as x from the surface of the mirror, but as - if measured in the 

 opposite direction. In the case of a concave mirror and an object in front 

 giving a real image (fig. 181), both y and/ are of the same sign as x, or all 

 three are +. But with a convex mirror (fig. 179) y and /are both opposite 

 in sign to x, i.e., both are - ; with a concave mirror forming a virtual image 

 (fig. 180), yis -, whilst/ is +. 



