FOCAL LENGTH OF ENGLISH OBJECT-GLASSES. 269 



plain English thus : — The solar focal length, when a small 

 lens is used and the image is greatly magnified, by dividing 

 the distance between the object and image by the number of 

 times the object is magnified, increased by 2. 



Example. — Suppose a screen is 100 inches from an object, 

 which is found by measurement to be magnified upon the 

 screen 60 times : what is the focal length (solar) of the lens ? 



/ = g^^ nearly = 100 -^ 62 = 1-6129. 

 If greater accuracy is required, the divisor must be in- 

 creased by -, or — . 

 •' m 60 



Thus, 



f ioo m 1.61247 



/— 1 — 62-016667 — AOJ^-±<. 



6^ + 2 + 60 



The first approximation is true to three places of decimals. 



The converse property is also easily ascertained when the 

 image is considerably enlarged. Suppose the focal length is 

 known, and it is required to find the magnifying power at a 

 distance {d), then 



'^ o 

 m = -.— %. 



('Phil. Transact., p. 594, 1870.) 



Example ; / ^ 2 inches : what will be the magnifying 



power at 180 inches' distance of screen from object ? 



1 so 

 m = ^-2 = 90-2 = 88 nearly. 



If it be required more accurately, then the quadratic 

 equation 



m + 2 + — = -» 

 must be solved ; or, 



m^ + 2m + 1 = -^ : 

 or, / 



m2 - (4 - 2 ) ^ = - 1 ; 

 or, V ' 



The focal length of a very small single lens is rather diffi- 

 cult of measurement, as the refractive index as well as the 

 curvatui-es or radii of surfaces require to be accurately known. 



^ The positive sign must be taken, and the distance between object and 

 image cannot be less than four times the focal length, and then m has a 

 minimum value. 



