MATHEMATICAL SCIENCES SEVENTEENTH CENT. 157 



FIG. 61. 



Though the lines in the diagram 



light in passing obliquely from air into glass, and vice versa, he will 

 perceive, by a simple inspection of Fig. 59, the general effect of con- 

 vex and concave lenses in bending incident parallel rays toward and 

 from the axis. For on comparing these figures with the sections of 

 the various kinds of lenses, Fig. 60, it will be observed that the pieces 

 shown in Fig. 59 accurately represent zones or portions of the two 

 upper lenses. In Fig. 61 the 

 paths of three rays (out of an in- 

 definite number), emerging from 

 the point , are traced through 

 the double convex lens, by which 

 these three (and all the rest emerg- 

 ing from b) are made to meet to- 

 gether and cross each other in the 

 point a. The point a is said to 

 be the focus of the rays from b. 



are not continued, the rays of light would of course pass through a, 

 continuing their passage in straight lines, so that a would in effect be 

 a luminous point like fr, but limited as to the direction of the emitted 

 rays. The remaining line in the diagram represents what is called the 

 axis of the lens, an imaginary line passing through the centre. The 

 focus of incident rays emerging from a point is situated in the axis, 

 only when the point of emergence is also in the axis; in all other cases 

 the focus is on the side of the axis opposite to the luminous point. 

 This much being understood, the reader can have no difficulty in 

 tracing the formation of images by a lens. Thus in Fig. 62 we have 

 the inverted image 

 of a candle thrown 

 on a wall. Here 

 the image is larger 

 than the object ; 

 but by changing 

 the position of the 

 lens to a certain 

 point, an image 

 smaller than the 

 object may be ob- 

 tained, as shown in 

 Fig 63. It is easy 

 to verify these facts 

 by a common eye- 

 glass, or a lens of 

 a pair of spectacles. 

 The effect of a 



FIG. 63. 



combination of two lenses may be studied in Fig. 64 ; but here the 

 entire pencils of rays emergent from each point must be supplied in 



