USEFUL TO THE MICKOSCOPIST 1 1 23 





For boro-silicate glass /u, = 1-51 ; r = -5898/; and s = - 3'769/ ; (xvii) 

 S/= -1-042 ^ ......... 



For flint glass /tt - 1-62 ; r = -G53/; ands= -12'06/; (xvii) 



......... (XV ) 



Critical angle. Let & be the critical angle for a ray passing out of a 

 denser medium into a rarer one. 



Then sin 8 = - ......... (xviii) 



A 1 



When M = 1-333, 6 = 48 36f ; /* = | , = 4148 ; /z = l-52 = 41 8f ; 



^ = 1-62, = 38 7'. 



Let /be the principal focus, and _p = the distance from the object to 

 the optical centre of the lens, p' = the distance from the optical centre of 

 the lens to the conjugate image. 



Then f-*t* P=4^/, /--> ..... (xix) 



P-f P"f P+P 



Let v be the distance from the object to /, and w be the distance from 

 /on the other side of the lens to the conjugate image. 

 Then 



v = p-f; w=p'-f\ p = v+f; p' = w+f; and vw=f*\ v = -L 



w 

 f- 

 w= J - ..................... (xx) 



If o be the size of the object and i the size of its conjugate image 



/ v p p-f f 

 iv = if^ip^ if = i(p-f). 

 f w p' p'-f f 



^ o ^ + o + o i 



Examples: With an objective of J-inch focus it is required to project 



an image of a diatom -03 long, so that it may be 1'5 inch on the screen, 



what must be the distance of the screen from the optical centre of the lens ? 



,_/(i + o)_ -5(1-5 + -(M)_ 25 . g _ 

 o -03 



Therefore p' = 25- inches, the distance required (xxi) 



2 



Conversely, if the image of a diatom projected by a -inch objective 

 measures 2 inches on the screen at 40 inches from the optic centre 

 what is the size of the diatom ? 



.. 2x1 

 o= ' 1 J = f_ = -0125 , . . . (xxi) 



P'-f 40 1 - 1 " 80 

 4 4 



the size of the diatom required. 



4 c 2 



