USEFUL TO THE MICEOSCOPIST 1 1 23 



. 

 ' / 



For boro-silicate glass /* = 1-51 ; r = -5898/; ands = -3'7b'9/; (xvii) 



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



For flint glass /* = l'G2 ; r = -653/; and s = - 12-06/; (xvii) 



(xv) 



Critical angle. Let 6 be the critical angle for a ray passing out of a 

 denser medium into a rarer one. 



Then sin 6 = ......... ixviii) 



When p = 1-333, 6 = 48 30^'; M = , = 41 48i ; M = l-52 = 41 8f ; 



A 



^ = 1-62, (9 = 38 7'. 



Let /be the principal focus, and j; = 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 p--, *=; f - 



-, = --, 



P ~f P "/ P + P 



Let v be the distance from the object to f, 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=*~ 



f'~ 

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



V 



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



= of = op' of = o(p'-f) . 



~ 



* ~" 



_/ ~f 



p-f f 



if ^i(p -f) . 



f w p' p'-f f 

 _op'_f(i + o). ,_*_/(*+<>) . 



P ' . -- ; - > 1 J ~ > 



^ ^ o o 



of if f ip op' ow 



t; = -^; w=-*-; /=^-- =_i- .... (xxi) 



/. o ^ + o ^ + o ^ 



Examples: With an objective of |-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 ? 



+ o) = -5(1-5 + -08) = 9 . 



,., _ 



-03 



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



*J 



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

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

 what is the size of the diatom ? 



4 4 

 the size of the diatom required. 



1 ._> 



