BRIGHTNESS OF IMAGE 



and by direct illumination if 



113 



d = 



61 A 

 N.A. 



where A =wave length of light used. 

 Thus, in the middle of the spectrum, 



A = -00054 mm., 

 and N.A. in the very best lenses =1*6 ; 



from which it is apparent that it is impossible to distinguish, i.e. to resolve, any 

 two points less than '000103 mm. (approximately 0'1/x) apart, or to see the details 

 of an object of smaller dimensions than O'l/u. 



Limit of effective magnification. Now the eye can only easily distinguish 

 two objects as separate whose distance apart subtends an angle of 2' at its 

 nodal point. This is the angle which a distance of '1477 mm. subtends at 



10 inches. Then the necessary magnification is : 



1477 

 0001 ' 



1477. Consequently, 



the limit of resolution of the microscope is attained when the total magnifica- 

 tion is about 1450. With an high eyepiece a further magnification may be 

 obtained up to 1600 or 2000, or even 3000, but no more detail will be dis- 

 coverable. The effect of the higher magnification will merely make the 

 detail larger : it will add no new detail but will still further diminish the 

 brightness of the image. 



Resolving power oc , for it varies inversely as the least distance between 



Cv 



separable points. Hence, whatever the focus, the resolving power oc N.A., and 



(N A ) 2 

 comparing lenses of the same focus, the brightness of the image oc v ' 



6. Brightness of image. 



Suppose M and M' be the magnifications obtained, using the same objective 

 but different eyepieces, 

 and let M' =2500, and M = 1450. 



T>/ 



The relative brightness -^ of the image in the two cases will be 

 B 



IT (N.A)MN.A.) 2 (1450) 2 _1 



B* M' 2 M 2 c (2500j 2 ' ~"3 ; 



so that the penalty of increasing the magnification from 1450 to 2500 is to make 

 the brightness of the image -J what it was with the lower magnification. 



The penetrating power oc =^-r-, so that 

 N.A. 



