540 



Microscopy /29 : 2 



light of one of these bright lines can pass, the transmitted light will 

 spread out past the focal plane as if from a single line source. If, how- 

 ever, light from two of the lines in the focal plane is allowed to pass the 



Image Plane (+g) 

 [Magnified Real Image) 



Diffraction Order 



Focal Plane [+f) 



Lens [Objective) 



'—^—v—^j4 Grating [Object) (-/>) 



Figure 2. Grating and lens. This figure is used in derivation 

 of the limit of resolution of a lens such as the objective lens of 

 a microscope. 



screen, interference will occur. The interference pattern will have just 

 the proper form to give rise to an image of the original grating, pro- 

 vided that the latter was more than a focal distance from the lens. In 

 fact, the image will occur at a distance q given by the lens formula 



111 



q P~f 



(2) 



In this, — p is the distance from the grating to the lens and / is the 

 focal length of the lens. The plane at q is called the image plane of the 

 objective. 



If the spacing of the grating is decreased, the number of bright lines 

 in the focal plane will also decrease because sin 9 cannot exceed one. As 

 this happens, the distance between the various diffraction orders 

 increases. In the extreme cases, even the first-order diffraction line will 

 disappear, leaving only the central line. When this occurs, no image of 

 the grating can be formed by the lens. 



