OPTICS. 



11 



focal distance C/is the same as in con- 

 vex lenses, and when the lens is une- 

 qually concave, the focal distance will 

 be found by the rule for unequally con- 

 vex lenses. 



When converging rays proceeding to 

 a point F, (Jig. 1 1,) beyond the princi- 

 pal focus O of a concave lens, are in- 

 tercepted by it, they will be made to di- 

 verge in lines L r, L r, as if they pro- 



Fig.ll 



ceeded from a focus/ in front of the 

 lens beyond O. When F coincides with 

 O, the refracted rays L r, L r will be 

 parallel, and when the point F is within 

 O, the refracted rays will converge to a 

 focus on the same side of the lens with 

 F, but on the other side of O. These 

 foci, viz. F and f, are called conjugate 

 foci, and the position of one of them, 

 when the other is given, may be found 

 by the rule for converging rays falling 

 on convex lenses. 



When diverging rays R L, R C, R L, 

 (fig. 12.) proceeding from any point F 



without the focus O N, fall upon a con- 

 cave lens L L, they will diverge in direc- 

 tions L r, L r, as if they proceeded from a 

 point/, between O and C ; and as F ap- 

 proaches to C,/ will also approach to it ; 

 and the distances FC or/C will be 

 found when either of them? is given, by 

 the same rule as for diverging rays fall- 

 ing upon convex glasses. 



^Refraction through a Meniscus and 

 a Concavo-convex Lens. The effect of 

 a meniscus upon light is the same as a 

 convex lens of the same focal distance ; 

 and that of a concavo-convex lens is 

 the same as that of a convex lens of the 

 same focal distance. The following is 



the rule for finding their focal lengths 

 for diverging rays. Multiply double the 

 distance of the point of divergence by 

 the product of the two radii for a divi- 

 dend ; take the difference between the 

 products of the above distances into each 

 of the radii for a divisor, and the 

 quotient will be the focal distance re- 

 quired. 



For parallel rays, the rule is much 

 simpler. Divide twice the product of 

 the two radii by the difference of the 

 radii, and the quotient is the principal 

 focal distance. 



In studying the preceding account 

 of the refraction of light through lenses, 

 we would recommend it to the reader 

 to demonstrate to himself the truth of 

 1he different results, by actually pro- 

 jecting -the rays in large diagrams, and 

 determining their course after refraction 

 by the method shown in figs. 4 and 6. 

 He will thus obtain a knowledge of the 

 progress of light through refracting 

 surfaces, which will facilitate the study 

 of the following chapters. 



The property of a convex lens of re- 

 fracting parallel rays to a focus fur- 

 nishes the principle upon which the 

 burn ing glass is constructed. A burning 

 glass, indeed, is nothing more than a 

 large convex lens, L L, (Jig. 7.), which 

 collects into a small space, at its focus/, 

 all the rays of the sun R L, R C, R L, 

 which fall upon it. 



If the lens L L has a surface of 400 

 square inches, and if the rays which 

 cover its surface are collected into a 

 space of one square inch, the burning 

 power will be 400 times, provided no liurht 

 is lost, and all the rays are collected in one 

 spot. It is both difficult and expensive" 



