OPTICS 



259 



point of the directing rays, or the nodal point. The chief ray 

 drawn through the vertex of the refracting surface is called the 

 optical axis. 



O 



FIG. 26. 



4. Rays parallel with the optical axis may be regarded as coming 

 from an infinitely distant object point lying in the axis. After 

 refraction they unite at a point on the optical axis, called the 

 second focal point; its distance from the surface is called the 

 second focal distance. Rays which, after refraction, run parallel to 

 the optical axis, pass, before refraction, through the first focal 

 point, whose distance from the surface is called the first focal dis- 

 tance. As in the formula for this case a 1 or 2 is oo , the focal dis- 

 tances designated by_/~ a and/j are 



f = 

 ./ 1 ~~ 



J i 



The vertical planes erected upon the optical axis at the focal 

 points are called \hQ focal planes. 



5. Construction of the image of a given object. 



Let mm (Fig. 27) be a spherical surface separating the two media 

 M l and M . Let K be the centre of curvature. AB is the optical 



FIG. 27. 



axis of the system, F 2 the second, and F l the first, focal point. To 

 find the image of the luminous point O l , draw the directing ray 

 O^K. Also draw a ray from O l parallel to the optic axis ; this 

 cuts the surface at h l9 and from k l passes through F^ and its prolon- 

 gation cuts O^K at i_, which is the image point. In a similar way 

 the image point 2 of the luminous point 6> 2 is found. The image 

 formed in this case is real and inverted. 



