384 REFLECTION OF LIGHT. 



The reflected rays will still diverge, but not so rapidly as the incident 

 rays. If the divergence be less than that first mentioned, viz., that 

 of rays issuing from a point further from the mirror than the prin- 

 cipal focus, the divergence will be changed to convergence and a 

 real focus will be formed. 



601. The Principal Focus. The focus of a con- 

 cave mirror is the point toward which the reflected rays 

 converge. All incident rays parallel to the principal axis 

 will, after reflection, converge at the principal focus. The 

 principal focus is the focus of rays parallel to the 

 principal axis. The rays will be practically parallel 

 when their source is at a very great distance, e. g., the sun's 

 rays. Solar rays coming to the human eye do not diverge 

 a thousandth of an inch in a thousand miles. 



(a.) Above we stated that parallel rays would be made to converge 

 at the principal focus of a spherical concave mirror. This is only 

 approximately true ; it is strictly true in the case of a parabolic 

 mirror. In order that the difference between the spherical and the 

 parabolic mirror may be reduced to a minimum, the aperture of a 

 spherical mirror must be small. The case is somewhat analogous 

 to the coincidence of a circular arc of small amplitude with the 

 cycloidal curve ( 144, a). A source of light placed at the focus of 

 a parabolic mirror will have its rays reflected in truly parallel lines. 

 The head lights of railway locomotives are thus constructed. Para- 

 bolic mirrors would be more common if it were not so difficult to 

 make them accurately. 



602. Conjugate Foci. Kays diverging from a 

 luminous point in front of a concave spherical mirror and 

 at a distance from the mirror greater than its focal distance, 

 will converge, after reflection, at another point. The focus 

 thus formed will be in a line drawn through the luminous 

 point and the centre of curvature. In other words, if the 

 luminous point lie in the principal axis, the focus will also ; 

 if the luminous point lie in any secondary axis, the focus 

 will lie in the same secondary axis. The distinction be- 



