CONSTANTS OF A LENS. 



335 



When the thickness t of the lens is taken into account, equation 

 (2) becomes 



' + ' 2 



Pi -i t P3 + t 1'l 



This combined with (1) and (3) gives the relation 



. ., '. -^ (8) 



We have a similai' equation for the reversed position of the lens, and 

 also, for direct refraction through the lens, the equation (correspond- 

 ing to (6) above) 



3/ri + Azi)_ i/(x + ii=i)^_i (9) 



/ \ 2i n / / V ?2 r., J (I 



iji and q.2 being the respective distances of the light and its image 

 from the front and back faces of the lens. These equations are strictly 

 rigorous and can be worked outto any desired degree of accuracy. 



The most favorable values of pi and ^^4 for minimizing the errors 

 of experiment, are when pi — Pi i.e. when the light is placed at the 

 center of curvature of the equivalent mirror. In this case, any 

 ray of the pencil is reflected normally at the back surfiice of the 

 lens, and returns along the same track. Further this gives at once 

 ]h = Pi '^ Ph and (8) reduces to 



lit lit' 



u- 



-^ 



+ 



n 



_ 



'l 







''\- 



- 1 



u~ 



.1 



+ 



n 



+ - 



Thus the results in (7) are to be corrected to the first order of 

 small quantities, by diminishing I///1 by u^l'^'l '''Hd similarly l//?2 

 by ixihi 



As for —7-, the correction is given by 



J \__ 





