113 



The Black and White Dot Phenomenon. 



By J. Rheinberg, F.R.M.S. ^^--^J**^ 



{Read Ajjril Idth, 1901). 



The origin of the black and white dot phenomenon in diatoms, 

 when the focns is adjusted to different shades, arises, I believe, 

 primarily from the fact that the perforations in a diatom form 

 approximately vertical partitions between two media differing in 

 refractiv^e index. Wherever two media of unlike refractive index 

 form a vertical wall or boundary upon which a cone of light 

 impinges from below, a solid area on both sides of the plane 

 of partition is filled with darkness. This comes about as 

 follows. A certain portion of the light which impinges on the 

 partition from the side of the denser medium is not refracted 

 through it ; instead of this it is reflected, just as if the vertical 

 wall were an ordinary mirror. The light which behaves in this 

 way is that which reaches the plane of partition beyond the 

 " critical angle." In consequence hereof darkness is brought 

 about on the less dense side of the partition, in the space 

 where the light has been unable to get through, from the side 

 of greater density. And darkness is also brought about on 

 the denser side of the partition because throughout the whole 

 of a certain solid space a direct and a reflected wave-stream, 

 emanating from the same points of the light source, meet in 

 opposite phase. 



A few diagrams, drawn exactly according to the laws of 

 refraction, will make the above explanations more clear. In 

 Figs. 1-3 the diatom is denser than the imbedding medium ; in 

 4-6 the imbedding medium has the higher refractive index ; and 

 the cases represented are — where light impinges on a diatom 



(Figs. 1 and 4) at an angle less than the critical angle 



( ,, 2 and 5) at the critical angle; 



( ,, 3 and 6) at an angle greater than the critical angle. 



In all these diagrams the closely shaded portion (when un- 

 crossed by other lines) shows where no light has been able to 

 get through, and it will be seen that no light reaches a space 



