120 Dr Searle, The determination of the focal 
prevent any view, through the microscope, of its image, the scale 
reading of the microscope carriage corresponds to A and not to B. 
The observations are facilitated by proper illumination of the 
grains. The best illumination is obtained if a strong beam of 
light is made to fall upon the grains in a direction nearly 
tangential to the surface of the mirror. 
Let AB=~2 and let « be positive when B lies in front of A. 
Then, if AC =p, we have BC = p — a, and thus, by (3), 
:5 = Lee (4) 
Hence | pte so Scscocccc >: (5) 
Thus f is nearly equal to 4p when a/p is small. ; 
If the distance of H from A be h, and if h be counted positive 
when H lies in front of A, we have 
h=p-2f= oe age (6) 
Thus h is nearly equal to 4 when a/p is small. 
§ 6. Practical example. The following results were obtained 
In an experiment by Mr Heath upon an ordinary glass concave 
mirror silvered at the back. 
Distance of centre ( from vertex A, 19°70, 19°65, 19°65 em. 
Hence p=19-67 cm. 
Reading of carriage when microscope is focused on lycopodium at A; 
1-27, 126 cm. Mean reading 1-265 cm. 
Reading of carriage when microscope is focused on image of A, 0°32, 
0°31, 0°30 cm. Mean reading 0°310 cm. 
The image of A was behind A. Hence 
#= — (1265 — 0°310) = — 0-955 em. 
Then, by (5), 
_ p(p—#) 19-67 x 20-625 
Des 29-2 40-295 
To find the position of the principal point H relative to the vertex A, we 
have, by. (6), 
= 10:07 cm. 
IB USOT OOD 
Leona 7 0°47 cm. 
Hence the optical system is equivalent to an ideal concave mirror of focal 
length. 10-07 cm. or of radius 20-14 cm, placed with its reflecting surface 
0°47 cm. behind the front surface of the glass mirror, 
§ 7. The micrometer method. This method corresponds to the 
micrometer method of measuring the focal length of a lens system, 
a method recommended by Mr T. H. Blakesley *. 
* Geometrical Optics, p. 91. 
