COLOURS OF THIN PLATES. 147 



of the rajs of this second pencil, meeting the ray DM of the 

 first at the point M ; and let us calculate their interval of re- 

 tardation. The latter has traversed the space AB + BA in 

 glass, and AM in air ; while the former has described the 

 space AC + CD in glass, and DM in air. The interval of 

 retardation is therefore the time of describing AM - DM in 

 air, plus the time of describing 2 (AB - AC) in glass ; and it 

 is easy to prove that the corresponding space in air is equal 

 to 



a (2b + fia) 9 



in which a denotes the distance, OA, of the screen from 

 the plate ; b the thickness, AB ; and y the distance, OM, of 

 any point on the screen from the aperture. Equating this 



to n -, it follows that the successive bright and dark rings 

 will be formed where 



When a is very great in comparison with 6, as is usually the 

 case, we have simply 



tf 



2t> 



(161) The phenomena of the colours of thick plates have 

 been reproduced by M. Babinet under a more instructive 

 form. 



The rays proceeding from a luminous point are refracted 

 by a lens, and are then received upon a transparent plate 

 with parallel surfaces, interposed between the lens and its 

 focus. If now this plate be slightly tarnished, or covered 

 with powder, a series of concentric rings will be formed 

 around the focal image. The innermost of these is white ; 

 and this is followed by a series of coloured rings in the order 



L2 



