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Dr Searle, The determination of the focal length, etc. 115 
The determination of the focal length of a thick mirror. By 
G. F. C. Searwe, Sc.D., F.R.S., University Lecturer in Experi- 
mental Physics, Fellow ‘of Peterhouse. 
[Read 8 February 1915.] 
§1. Introduction. The experiments described in the following 
paper bear the same relation to those made upon an ideal spherical 
mirror as the measurement of the focal length of a thick lens or 
of a lens system bears to the measurement of the focal length of 
an ideal thin lens. They thus form a useful introduction to 
experimental work with lens systems. 
The properties of mirror systems are simpler than those of 
lens systems, since a lens has two foci, two principal points and 
two nodal points, while a mirror has only one focus, one principal 
point and one nodal point, the latter being what is called the 
“centre” of the mirror system in § 4. 
The first method (§ 5) was introduced into my practical class 
at the Cavendish Laboratory in 1908; the other two methods 
(§§ 7, 9) were devised after the paper was “read.” 
§ 2. Jdeal mirror. When a concave spherical mirror is 
formed of metal or of polished silver deposited on the front 
surface of a spherical surface of glass, the reflexion takes place 
at the surface. If wu and v be the distances of an object point 
P and its image @ from the vertex, i. the point in which the 
surface of the mirror is cut by the straight line through the two 
points, 
where the constant / is called the focal length of the mirror. 
Here w and v are counted positive when P and Q are on the 
same side of the vertex as the centre of the spherical surface. If 
we make w infinite, then v =f, so that f is the distance from the 
vertex to the point to which parallel incident rays are reflected to 
a focus. 
If we put w=0 in (1), we find v=0, and thus the vertex is 
a self-conjugate point. 
If we put w= 2, we find that v = 27; and thus 
U=v=2F 
gives a second self-conjugate point. Hence, if we place an object 
point in such a position (not in contact with the mirror) that it 
coincides with its own image, the distance of the point from the 
mirror is 2f. 
