ON INTERFERENCE IN THE MICROSCOPE. 



13 



left-side at right angles with the object; then, after passing 



through ab, a portion only of the rays will continue in their 



original straightforward course, while another portion will 



be deflected and form divergent pencils which completely 



occupy a given angular space. In the figure one such diffracted 



beam is shewn with a divergence angle of 30°. Suppose, now, 



the width of al=-i mik., and the wave length ai of the incident 



light (homogeneous) =J mik, 3 then ai: ah : : sin. 30** : r ; con- 



, . sin. 30° _ , , 



sequently az= . ao^=i wave length. 



If we separate the diffracted pencil into two equal halves by 

 drawing a line from the middle point of ah parallel with the 

 marginal rays, it will at once be seen that each ray in each of the 

 halves will be displaced by half an undulation from the corres- 

 ponding ray of the other half.* The co-operation of the two 

 halves must necessarily, therefore, produce darkness if all the 

 rays are brought 



together by Fig. 2. 



suitable refrac- 

 tions. If, for 

 example, we 

 focus a micro- 

 scope objective 

 on the object, 

 then a dark 

 band will appear 

 in that part of 

 the focal plane 

 in which the 

 rays of the 



diffracted pencils unite. This is the first dark band which form ^ 

 itself next to the line of light which the undiffracted incident rays 

 produce in the focus of the objective. 



See also Tyndale's six Lectures on "Light," 1873, pages 81. 



