8 OS THE APPLICATION OF INTERFERENCE METHODS 



forming a spectrum from which any required radiation may be separated 

 from the rest by passing through the sht S.* 



The hght from S is rendered nearly parallel by a eollimating lens, and 

 then falls on a transparent film of silver, on the surface of the plane parallel 

 plate Gi.f Here it divides, part being transmitted to the fixed plane miiTor 

 Ml, and part reflected to the movable mirror J/,. These muTors return the 

 light to the silvered surface, where the fii'st pait is reflected, and the second 

 transmitted ; so that both pencils coincide on entering the observingtelescope.J 



A little consideration will show that this an*angement is, in all respects, 

 equivalent to a film or plate of air between two plane surfaces. The inter- 

 ference phenomena are therefore the same as for such an air-plate. 



The theory of these interference bands has been given in an article 

 entitled "Interference Phenomena in a New Form of Refi-actometer," PJiilo- 

 sophical Mdfiazme for April, 1882. As is there sho-wn, the projections of the 

 bands are, in general, conic sections, the position of maximum distinctness 

 being given by the foi-mula 



P= -^taii i cos' 

 tan'f 



in which f„ is the thickness of the equivalent air-plate, where it is cut by the 

 axis of the telescope, 'f , the inclination of the two surfaces, 61 and /, the com- 

 ponents of the angle of incidence i)arallel and pei-peudicular respectively to 

 the intersection of the sui-faces, and F, the distance of the plane of maxi- 

 miun distinctness from the surfaces. If be small, the variations of P 

 with may be neglected, and we have then 



F = — "- tail i, 

 tan 'f 



or with sufficient accuracy, 



? 



• In the case of close groups of lines, the image of the source is first thrown on a slit ; otherwise, the 

 lines at .S' would overlap. 



t The lifht entering the telescope is a maximum when the thickness of the silver film is such that the 

 intensity of the transmitted liglit is equal to that of the retieeted light. The silvering has another im- 

 portant advantage in diminishing the relative intensity of the light reflected from the other surface. In- 

 deed, for this purpose, it is advisable to make the film heavier ; even so thick that the reflected light is 

 twice as bright as the transmitted. This does not affect the ultimate ratio of intensities of the interfer- 

 ing pencils ; for what is lost by transmission on entering llie plate <V, is made up by reflection on leaving 

 it, the effect being simi)ly to diminish somewhat the whole intensity. Another advantage of the thicker 

 film is that it can be made uniform with far less dillicnlty tlian the thin film. It ni.ay be mentionod that 

 with this form of instniment the interference fringes in white hght present a purity and gorgeousness 

 of coloration that are surpassed only by the colors of the polariscope. 



t The second plane parallel plate G,_. is made of the same thickness as the first, and is required to 

 equalize the optical paths of the two pencils. 



