Nov., 1915] Making a Photographic Objective 



15 



Note 1 — ^A Spherometer for Short Radii. 



In Fig. 6, A is a regular Brown & vSharpe Micrometer Head with the measuring 

 point ground to an angle of 60° and slightly rounded; B is a round steel base all 

 machined at one setting in which the micrometer head is clamped by a set screw 

 not shown. 



Oy 



Fig. 6 



Let r be the radius of the spherical surface, MNO, and we will have at once 

 r= (a^ + d^) / 2d. The advantage of this form of spherometer is that it is very 

 easy to make the point of the micrometer exactly central with the base and the 

 value of 2a can be accurately determined by means of an ordinary micrometer 

 calliper. For a convex surface, 2a should obviously be the inside diameter of 

 the base, B. 



In using the instrument, two tables, one for concave and one for convex 

 surfaces, should be prepared; these tables to give the power in dioptres for each 

 one thousandth of an inch in the value of d. Using the American Optical Co.'s 

 Standard Index, namely, n ecjual to 1.5000 and one dioptre as being the power of a 

 lens of 40 inches focus, we have, for a piano lens, p = 40/f = 40d/(a^-|-d2) since 

 f = r/(M-l). 



The advantage of forming the table in dioptres in place of radii directly is 

 that the tabular differences are small at all parts of the table so that interpolation 

 can be readily done and this is not the case in tables which give the radii directly. 



If upon measuring the radius of the tool or lap being turned in the sphere 

 turning machine, Fig. 4, with this spherometer, the tool is found to be in error by 

 an amount Ap this may be corrected by changing the position of the cutting 

 tool by an amount 20Ap/p^. 



