152 



ELEMENTS OF LABORATORY WORK 



back of the mirror together with the image of those in front. 

 Place the two cross-wires so that the image of the one in 

 front appears to coincide with the visible portion of the one 

 behind, and adjust carefully until the coincidence is main- 

 tained when the eye is moved from side to side. 



Instead of two cross-wires, two pins fixed vertically, one in 

 front and one behind the mirror, may be used. They are 

 placed so that the upper part of the one behind is visible, and 

 may be compared with the image of the lower part of the one 

 in front. 



If the distances of the objects from the mirror be now 

 taken, they will be found equal. If the law of reflexion 

 stated above be assumed to be true, then the results here ob- 

 served would follow, and hence we may consider the law to be 

 indirectly demonstrated by these experiments. Let a b be the 

 plane mirror, and c and d the cross-wires, at an equal distance 

 in the same straight line from the mirror. Then assume a 

 single ray of light, from the point of intersection of the wires 

 in c, to be reflected, after meeting the surface at e, making 

 the angle ceg equal to the angle feg, when ge is the normal 



at e. Then it is easy to prove 

 by geometry that the line f e, 

 continued will meet the cross- 

 wires d at their point of inter- 

 section, for the angles c e k and 

 d e k are equal (d e k being 

 equal to a ef), and d k e is 

 equal to eke, each being a 

 right angle, and ke common 

 to the two triangles e k d, eke. 

 Therefore the triangles are equal, and likewise dk to kc. 

 Hence the eye placed anywhere on the line ef will perceive 

 the object d, and the image of c at the same position, provided 

 only the law be true. 



98, To find the Focal Length of a Concave Mirror and of 

 a Convex Lens. A needle or pin is fixed vertically in front 

 of a concave mirror, and the position, in which the eye will see 

 an inverted image of the needle, is found. It is advisable to 



