323 Mr. J. Bridge on the Diffraction of Light. 



(1) The problem may be stated as follows : — A series of waves, 

 plane or spberical, meet in their course an aperture of given form ; 

 it is required to find the actual or virtual intensity of light at 

 any given point. 



The answer according to the undulatory theory is, — let a 

 sphere be described having the given point as centre ; then the 

 displacement (actual or virtual) at the given point is proportional 

 to the geometrical sum of the displacement simultaneously exist- 

 ing on this sphere, and the intensity as the square of this dis- 

 placement. For example, if the given point be on the side 

 towards which the light proceeds after leaving the aperture, the 

 displacements simultaneously existing on the sphere referred to 

 will all, when equally modified by distance, reach the given point 

 together. 



I shall take as the normal case a series of parallel waves fall- 

 ing on the aperture, and viewed either by the naked eye, or by 

 a telescope in focus. It will then be necessaiy to sum the dis- 

 placements simultaneously existing on a plane making a given 

 angle a with the aperture. This will determine the intensity of 

 light proceeding in the direction of the normal to the plane, and 

 brought to a focus at a distance /« from the pi-incipal focus. 



(2) The plane, which is perpendicular to the plane of the aper- 

 ture and to that in which we have to sum the displacements, 

 meets the aperture in a line which we may call the axis of x ; 

 also let y be the breadth of the aperture perpendicular to this at 

 the distance x. Then the aether in the plane of the diaphragm 

 being all supposed in the same state of displacement. 



J 



ysin— {vt — a.x)dx 



is the sum of the displacements which will at last coincide in 

 the image plane at the distance fa. from the focus. 



The intensity of the light at this point is A^ + B-,. where 



. C 2'7rax , , T, C ■ 2'Jreix , 



A= \y cos — r- — ax, and B = — I 2/ sin — - — . ax. 



(3) If there be two apertures, one of which may be converted 

 into the other by moving every y in the direction of its length, 

 or multiplying them all by the same ratio, they will give the same 

 diflFraction image in the direction (reckoning from the principal 

 focus) of the axis of x. 



For example, two triangles having the same altitude, and either 

 equal or unequal bases, give the same changes of intensity in the 

 focal line perpendicular to the base ; for the displacement in a 

 given plane arising from any point of the aperture is not altered 

 by moving that point parallel to the plane ; and in the second 



