22 
On the Limits of the Optical 
magnitude of the image to which the rays passing through that 
medium belong, remain unchanged by every refraction, provided 
always that the conditions of production of an accurate image are 
duly preserved. This product will therefore have the same value 
after emergence of the rays as it had before they entered the system 
of lenses. 
Demonstration. 
Let ah he the axis of a lens system, 
h h' one of the refracting surfaces, 
c the centre of its curve, 
a the point of convergence of rays, incident on h h', 
h the point of reunion of rays refracted by h h\ 
f the front principal focus, 
g the back principal focus. 
Further, let n represent the ratio of refractions of the medium in 
front of h h', 
n" represent the ratio of refractions of the medium 
behind h h', 
a the positive divergence angle h' ahoi the ray passing 
in first medium through Ti, 
a the negative divergence angle, in second medium 
—h'bh, 
/3' the magnitude of image a a" belonging to the rays 
of the first medium, 
P" the magnitude of image — b' b" belonging to the rays 
of the second medium. 
Firstly, we have, from similarity of triangles a a" c and b b" c, 
