32 



OPTICS. 



another (for if the paper were removed 

 they would cross one another at that 

 point). Then if the lengths of their 

 paths (or the distances between the 

 paper and the two radiant points) are 

 the same, they will form a bright spot or 

 fringe of light, having an intensity 

 greater than that which would have 

 been produced by either portion alone. 

 Now it is found that when there is a 

 certain difference between the lengths 

 of their paths, a bright fringe is pro- 

 duced exactly similar to what is pro- 

 duced when their lengths are equal. Let 

 us represent this difference by the letter 

 d, then similar bright spots or fringes 

 will be formed when the differences in 

 the lengths of the paths are 2d,3d,4 d, 

 5 d, &c. But, what is very remarkable, 



it is clearly proved that'if the pencils of 

 light interfere at intermediate points, or 

 at those points in their paths when the 

 differences in the lengths of the paths 

 are j d, H d, 2 d, 3 J d\ then, instead of 

 adding to one another's intensity, the 

 two pencils of light destroy each other, 

 and produce a black spot or fringe. 



This curious property of light has a 

 striking analogy with the beating of two 

 musical sounds nearly in unison with 

 each other, the beats corresponding to 

 the luminous spots or fringes, and the 

 cessations of sound between the beats, 

 to the black spots or fringes. 



M. Fraunhofer has found the follow- 

 ing to be the values of e?for the different 

 colours of the spectrum. The measures 

 are in decimals of an English inch. 



Colour. Lines in Fig 



Red C 



Orange yellow D 



Green E 



Blue F 



Indigo G 



Violet H 



In the theory which supposes light to 

 consist in the vibrations or undulations 

 of a highly elastic medium, and which is 

 now supported by many arguments, the 

 quantity d, or the difference in the 

 lengths of the paths, at which the inter- 

 fering pencils of light either destroy 

 one another, or unite their effects, that 

 is, at which they produce the black and 

 light fringes, is also the breadth of an 

 undulation or a wave of light. 



Those who do not adopt the system 

 of undulations, must, as M. Fraun- 

 hofer* has remarked, admit that the 

 quantity represented by d is a real, abso- 



Values of d, or Breadths < 

 Inch. 



'a \Vave of Light. 



0.000025S2 



0.00002319 



0.00002073 



0.00001912 



0.00001692 



0.00001578 



1. When we consider how glass is 

 ground and polished, its surface cannot 

 be mathematically correct ; but as long 

 as the inequalities, in reference to their 

 distance from each other, are less than 

 the magnitude d, they will not be detri- 

 mental either to the light which is trans- 

 mitted, or to that which is reflected, 

 and no colours of any kind can be pro- 

 duced by them. It would likewise be 

 impossible by any means to render in- 

 equalities of such a size visible. 



2. Hence, we may deduce the smallest 

 magnitude which can be rendered vi- 

 sible by a microscope. For if any ob- 



lute magnitude. Whatever meaning is ject whose diameter is d, consists of two 



i , . i "\ _ /_ n , 11 _.!__ __ j 



parts, it cannot be recognised as consist- 

 ing of more than two parts. In red light, 

 therefore, the limit of microscopic vision 

 is the thirteen-millionth -part of an Eng- 

 lish inch, and in violet light the eight' 

 millionth part of an English inch. 

 3. From these considerations, it fol- 



attached to it, it necessarily follows, 

 that one half of it in reference to the 

 effect is opposed to the other half, so 

 that if the anterior half combines ac- 

 curately with the posterior half, or inter- 

 feres with it in this manner under a 

 small angle, the effect of each is de- 

 stroyed, whereas that effect is doubled lows, that since the quantity d is greater 

 if two anterior, or two posterior halves in red light than in any other, the im- 

 combine, or interfere in the same man- perfections of refracting and reflecting 

 ner. From this determination of the 

 quantity d some important practical 

 results may be derived. 

 1. With respect to the influence of the 

 inequalities of polished surfaces in 



refracting and reflecting light. 



2. With respect to the limits of micro- 

 scopic vision ; and 



3. With respect to the colours which are 

 most suitable for delicate observations. 



* Edinburgh Journal of Science, No. xiv. p. 213 



surfaces will have less effect in injuring 

 vision when it is performed by red light, 

 than when it is done by any other rays 

 of the spectrum. On the other hand, 

 if these imperfections are made less 

 than d by skilful workmanship, a close 

 double star, which could not be seen in 

 red light, might be rendered visible in 

 violet light, provided always that there 

 be no want of light. 



