lO Gee and Adamson, Dioptriemcters. 



to the scale is i/io metre, we have, following the notation 



already used : — 



x= i/io 



and fl!= lo scale divisions 



— \\x. 

 Thus the required condition is fulfilled, so that S = D. 

 Also, the radius of the zero circle being 20 mm., is equal 

 to l/;tr+ \ly. 



Hence, the power of the lens can be read off directly, 

 as already explained, and it will be evident that the scale 

 divisions marked + will correspond to convex lenses and 

 the — divisions to concave lenses. 



In proving that the readings on the scale of the 

 instrument are the dioptric powers oi the lenses tested, 

 the following assumptions and approximations are made : 



(i) It is assumed that rays passing through a lens at 

 a fixed distance from the centre are equally deviated. 



(2) It is assumed that the tangent of the angle of 

 deviation is equal to the sum (or difference) of the tangents 

 of two angles whose sum (or difference) is the angle of 

 deviation. 



(3) It is assumed that the point of intersection of the 

 incident and emerging rays of light is in the plane of the 

 aperture. 



These assumptions will only be strictly accurate if the 

 lens is indefinitely thin, and if the rays of light pass 

 through the lens indefinitely near its centre. The instru- 

 ment is therefore only approximately correct in principle, 

 the errors being greater when the lens is thicker and more 

 powerful. 



The ordinary methods of determining the focal lengths 

 of thin lenses by means of the optical bank are also 

 inaccurate in principle, if the aperture and thickness of 

 the lens are not indefinitely small. 



