88 INTERFERENCE OF LIGHT. 



Two plane mirrors are placed so as to meet at a very 

 obtuse angle. A beam of light diverging from the focus of a 

 lens is suffered to fall upon them ; and there will be therefore 

 two reflected beams, whose directions are inclined at a very 

 small angle. Here, then, are two beams diverging from the 

 same luminous origin, separated simply by reflexion at plane 

 surfaces, without the intervention of edges, or of anything 

 accidental which can be regarded as contributing to the 

 result. These beams, however, still interfere, and produce a 

 succession of alternate bright and dark bands, in the manner 

 already explained. In order to satisfy ourselves that these 

 bands are in fact produced by the mutual action of the two 

 beams, we have only to intercept one of them, by covering 

 one of the mirrors, and the whole system instantly vanishes. 



Let Qn and Qn' 



represent the sec- / 



tions of the two Op- ::: - --A- 



mirrors, which we 



shall suppose to be '" :: - ^ 



perpendicular to the 

 plane of the dia- 

 gram ; and let k be the luminous origin, or the focus of the 

 lens in which the Sun's rays are concentred. Then taking 

 the points and O 7 at equal distances on opposite sides of 

 the mirrors, these points will be the foci of the two reflected 

 pencils, or the points of divergence of the two beams. Now 

 it is found, in the first place, that the bands are parallel to 

 the line of intersection of the two mirrors ; secondly, that 

 they are symmetrically placed on either side of a plane pass- 

 ing through this intersection, and through the point P, which 

 bisects the interval between the two foci and O 7 ; and 

 thirdly, that in proceeding from the mirrors, they are propa- 

 gated in hyperbolas, whose foci are and 0', and whose 

 common centre is P. 



