KY A. L. McAULAY, B.Sc, B.A., Ph.D. C)l 



SECTION 4. THEORY OF SECTION 3. 



Figure III. shows diagramniatically the slit D and the 

 lens E. Light falls on D normally, and therefore leaves 

 every part of it in the same phase. Consider a beam leaving 

 the slit at an angle with the direction of the incident light. 

 The distui'bances over a plane such as q perpendicular to this 

 direction will be brought together by E at Q, the point at 

 which a wave front at q would be focussed. The disturbances 

 over q at any instant will, however, not be in exactly the same 

 phase, and it is the combined effect of a set of out of phase 

 waves that will produce the illumination at Q. Let p, P be 

 the wave front, and focus for & = o. It is obvious that 

 this is the position of the image of the slit, that is, it is on the 

 vertical crosswire as adjusted in section 3. 



It is required to investigate the illumination at Q when 

 Q takes up different positions. For this purpose the slit 

 D will be thought of as made up of a large number of ele- 

 ments, and the combined effect of the wave trains from each 

 will be considered. The waves arriving at Q will be re- 

 presented as vectors in the usual way, and, as there are an 

 equal number of wave lengths between each element of q and 

 Q, a vector drawn for q will equally well stand for the effect 

 01* the same wave train at Q. a and b are two adjacent ele- 

 ments of the slit. Then obviously the path difference at q 

 of the light coming from a and b is .ib sin 0, and the phase 



difference of the wave trains at q (or Q) is ab sin 6. 



Now V(i = f sin = <\. Therefore, the phase difference be- 

 tween the wave trains is - 

 to the distance of Q from P. 



tween the wave trains is —a'. — r^ i.e., it is proportional 



Consider the vectors representing disturbances from suc- 

 cessive elements as short rods hinged to each other at the ends 

 (see Figure IV.). Then the line joining the ends of the 

 composite rod will be the vector representing the resultant 

 effect of all the elements. At P the waves are all in the samo 

 phase, the jointed rod or chain lies stretched out in a straight 

 line (Figure IV. 1), and the resultant is the arithmetic sum 

 of the components. At Q, from what has been said nbovo, 

 wave trains from adjacent elements will have a phase differ- 



once of " ai. . ^ ila say, i.e., each section of the chain will 



A t 



make an angle of ,]n with the one next to It. Obviously, 



