420 THE OUTGO OF ENERGY 



are in the principal axis two points so placed 

 that when the entering ray is directed toward 

 the first, the emergent ray will appear to come 

 from the second in a direction parallel to the 

 entering ray. These are termed nodal points. 

 In ordinary glass lenses the distance between the 

 two nodal points is about one third the thickness 

 of the lens. When this distance is so small that 

 it may be disregarded, the two nodal points may 

 be assumed to meet in an intermediate point 

 termed the optical centre (compare page 444) of the 

 lens. A ray directed to the optical centre is not 

 refracted but passes through the lens in a straight 

 line. The position and size of an image formed 

 by a lens can be found by drawing one line from 

 each extremity of the object through the optical 

 centre, and another from each extremity parallel 

 with the principal axis to the lens and thence 

 through the principal focus. The intersections 

 of these lines mark the position of the image and 

 its upper and lower limit. It is necessary to 

 remember that parallel rays are refracted through 

 the principal focus only when the aperture of the 

 lens does not exceed approximately ten degrees. 



Draw a horizontal line to serve as the principal 

 axis. Let a point near the middle of the line be 

 the optical centre of a double convex lens of 10 

 aperture and 5 cm. radius. The radius of curva- 



