448 Prof. Bar (on and Mr. Penzer on Simultaneous 



lantern and passes through the pin-hole S x (fig. 1) in a tin- 

 foil screen, falls upon the mirror M x of the optical lever, and 

 is thence reflected to the lens 1^ which focusses it upon the 

 photographic plate at R which is on rails in a dark room. 

 The normal to the mirror is M 1 N, and M] A shows the axis 

 about which it rotates if the bridge moves lengthwise of the 

 string. 



In the ordinary use of an optical lever as previously made, 

 the plane of rotation coincides with that of incidence and 

 the reflected beam describes an angle exactly double that 

 described by the lever. Or, if these angles are respectively 

 called 8 and /x, then 8/fi = 2. 



But in the special arrangement and use of the optical lever 

 here adopted, not only are the planes of rotation and incidence 

 inclined, but also the normal to the mirror is inclined to the 

 axis of rotation of the lever. Hence, as the lever turns, the 

 reflected beam traces out a conical surface instead of a plane. 

 And the angular magnification £//*, varies according to the 

 circumstances of the case between its limiting values unity 

 and infinity ! Thus when the lever turns through the small 

 angle /jl about its axis M x A, let the point N on the mirror's 

 normal rise to ~N' } and let R in consequence rise to R'. 

 Then since I, N' and R/ are in the plane of incidence and 

 reflexion, IN' R/ is a straight line. Hence 



RB//NN' = RI/NI . Also p = NN'/AN and 8 = RR'/AR. 



If we now write cc for the angle AM X N between the axis of 

 rotation of the lever and the normal to the mirror, and 6 

 for the angle of incidence I M x ~N, it can easily be shown 

 that the angular magnification is given by 



<> , 2 tan a 



8/fi: 



tan a — tan ' 



Thus, if the incident beam is coincident with the axis of 

 rotation, 6—— a and 8//jl=1. Again, if the incident beam 

 is along the mirror's normal, = and 8//n = 2 as in the 

 ordinary form and use of the optical lever. But if the angle 

 of incidence is nearly equal to a, the reflected beam is almost 

 coincident with the axis of rotation and the angular 

 magnification is very great. Thus writing 6 = a we have 

 S/^=co! ^ 



In dealing with the actual magnification of the arrange- 

 ment used, it is convenient to first omit the lens L] and find 

 as above how R would move to R' by the action of the 

 optical lever simply. Next trace this reflected beam back 

 through the mirror Mx to the virtual image of the pin-hole S x 



