168 Dr Searle, Experiments with a prism of small angle . 
adjustment may be completed by moving the goniometer arm. 
The observation is facilitated if a slit 3 or 4 mm. in width is 
placed near the burner. 
Fig. 12. 
For measuring the angle, a piece of glass millimetre scale is_ 
held against the frame supporting the vertical wire W of the 
goniometer, so that W is in contact with the divided face of the 
scale. To increase the distance to be measured, the flame should 
be placed so that both images are visible. It will be found that _ 
the two images move together with W when the goniometer 
arm is moved. 
If O (Fig. 12) be that nodal point of the lens which corresponds 
to the focal plane WU, then OW=f, the focal length. By the 
property of nodal points, OW and OU are parallel to the two 
parallel beams on the other side of the lens. Thus OW and OU 
correspond to PQ and RS in Fig. 11, and hence, in the case of 
Fig. 12, the angle (@) between the mirrors is 6=tr+4U0W. If 
WU=y, then 
The focal length of the lens may be measured by any of the 
usual methods, but it may be conveniently found without dis- 
turbing the goniometer. A single plane mirror is substituted for 
the double mirror of Fig. 12. As the arm of the goniometer is 
moved through any angle y, the image of the wire moves across 
the focal plane, the displacement of the image relative to the wire 
being the same as if the arm had been at rest and the mirror had 
been turned through the angle y. In this case the reflected beam 
is turned through an angle 2y. Thus, if a change of goniometer 
reading of a cm. corresponds to a change of reading of the image 
on the glass scale of b cm. and if / cm. is the distance from the 
centre of the pivot to the scale, we have b/f=2a/I or 
f= ba :2sh. (21) 
