316 PHYSIOLOGICAL PHYSICS. [Chap. xxv. 



focus, the rays after refraction will diverge : but 

 their backward prolongations will meet in the point F' 

 inside of the principal focus. The point F' is the conju- 

 gate focus (virtual) of F. If F' be the luminous point 

 its conjugate focus is F. 



The focal distance of lenses may be deter- 

 mined experimentally, and may be calculated. Thus, 

 if a convex lens be caused to intercept rays of light 

 from the sun, a well-defined luminous point may be 

 thrown on a screen placed at a proper distance on 

 the other side of the lens from the source of light. 

 The distance of the screen from the curved surface 

 when the luminous point is quite distinct, is the focal 

 distance. The focal distance may also be calculated, 

 if the conjugate foci be known, from the formula 



1 l 1 

 P p f ~ f* 



where p and p are the conjugate foci, and f is the 

 principal focal distance ; the formula, as given, applies 

 to convex lenses, provided the source of light p be 

 farther from the lens than the focal distance. When 



the source of light is nearer than the focal distance, -/ 



P 



is negative. For concave lenses the formula becomes 



1 1 1 



P' ~ P ~ f ' 



Formation of images by lenses. The for- 

 mation of images by lenses exhibits similar rules to 

 those observed in the formation of images by reflection 

 from mirrors. 



CONVEX LENSES. Let LL' (Fig. 145) be a convex 

 lens, c its centre, and F its principal focus, and 

 let AB be an arrow outside of the principal focus. 

 From A and B let rays parallel to the principal axis 



