326 PROFESSOR KELLAND ON THE THEORETICAL INVESTIGATION OF 



TT 2 e 2 X 2 b z 



.: total intensity = -- - x 





_vm j t/ + - _ -IN 



(that term which contains neither y nor 2 in 1 +^A _ _ _ y I) when m= oo) 



But y =0, whatever be y or z, when m oo . Hence the part 



x- 



of it which does not contain y or z is also. 



TT a 2 c 2 \ 2 6 2 X 2 6 2 

 .-. total intensity = - -^ = -ga- 2 x area of aperture. 



Hence we obtain D = \ 6. 



PROB. V. A series of plane waves are reflected at each of two equal mirrors in- 

 clined by an angle to each other, and are brought by a lens to a screen ; to 

 find the total intensity of light at the screen. 



Let x, y, z, be the co-ordinates of a point in the front of the wave ; p, q, those 

 of the point in the screen ; the origin being that point of the screen which lies in 

 the centre of the line joining the foci, whose distance is 2f, the axis of x being in 

 this line, and the plane of x y the screen. 



.: PM 2 =(-s 



P M = B b nearly, for the upper mirror. 



Similarly Q M = B + (/*""/) ( +f)-iy f or tne gecon^ yt being measured down- 



wards in this case. 



.-. the whole vibration due to the two mirrors is 



^ ff dx dy sin ?5 (vt. - B 

 D J J A 



* 



b 



vt - B - (p ~ f} ( *-- n ~ 



Let 2 1 be the length of the mirrors, g their breadth, measured perpendicular 

 to the axis of z ; then the limits are ir=g, x=0, tf=g, ^=0, y=l, y= I. 



