452 Mr. T. H. Blakesley on some Imjiroved 



the place where an object coincides with an inverted image of 

 itself. 



If the centre of curvature of the mirror coincides with the 

 second principal focus of the lens, the centre of the curvature 

 of ihe virtual plane mirror is at infinity; but the plane itself 

 will not be so, and its position rnay be easily found experi- 

 mentally as the place where an object coincides with an erect 

 image of itself. 



Such virtual mirrors, whether plane or not, giving erect 

 images, are of course often formed in front of the lens ; and 

 in such cases there is not the smallest difficulty in passing an 

 object u through the looking-glass." 



The rules given above for the position of the centre of 

 curvature and surface of the virtual mirror are equivalent to 

 the two following mathematical formulae : — 



The surface of the virtual mirror is situated at a distance 



fiom the first principal focus of the lens equal to — '- 



in a direction contrary to that in which the light is going 



before reflexion; and the centre of curvature of the virtual 



mirror is situated at a distance from the same point equal to 



f 2 

 — — • measured positively in the same direction. 



In these formulae / is the focal length of the lens ; r is the 

 radius of curvature of the mirror (positive if concave) ; k is 

 the distance from the second principal focus of the lens to 

 the principal focus of the mirror, measured positively in the 

 direction in which light is proceeding before reflexion. 



Now suppose that the mirror coincides in curvature and 

 position with the second face of the lens. This will be the 

 case if either that face is silvered or placed in a pool of 

 mercury. 



The position of the centre of curvature of the virtual 

 mirror can be found in the usual way, by coincidence with 

 inversion of the image and object. Let it be distant c from 

 the original first principal focus of the lens, positively measured 

 in the direction opposite to the light before reflexion. 



Then by the above formula 



k 2 



