ofL 



tight by 



Cylinders and k. 

 Table I. 



Spheres. 



i. 



6 in wave-lengths. 



A=2(r-«). 



0° 





100 



0° 



10° 





84 



0° 12' 



20° 





68 



0° 26' 



30° 





57 



0° 40' 



40° 





46 



0° 58' 



50° 





36 



1° 22' 



60° 





24 



2° 0' 



70° 





15 



3° 16' 



75° 





10-3 



4° 38 



76° 





9-2 



5° 3' 



77° 





7-7 



5° 41' 



78° 





67 



6° 11' 



79° 





5-4 



7° 0' 



80° 





3-9 



8° 9' 



80° 30' 





3-1 



8° 56'-4 



81° 





2-2 



10° 0' 



81° 30' 





1-1 



11° 38' -4 



81° 45' 





•55 



13° 3' 



673 



Although considerations of the phase change at total 

 reflexion will slightly modify the table given above, yet its 

 main features will remain unaffected. The path-difference 

 decreases very rapidly for small angles of deviation, but more 

 slowly for greater angles, so that the fringes will be narrow 

 at first and will broaden in oblique directions. 



The intensities of the refracted and the reflected rays can 

 also be calculated if we determine the width of the incident 

 parallel beams which respectively give rise to the refracted 

 and the reflected beams lying between the angles A and 

 A + rfA. If XA, X'A' (fig. 1) are the two rays incident at 

 angles i and i-\-di which are deviated by refraction through 

 the angles A and A + c<?A, and similarly YQ and Y'Q' are 

 the corresponding rays deviated through the same angles by 

 reflexion, the intensities of the beams between these extreme 

 rays must be proportional to AT and YQ ; respectively. 



Now AM = a "sin i; 



AT = a cos idi. 



But A = 2(r-t); 



dA = 2(dr-di) 



2 



fJb COS V 



(cosi —ft cos r)di. 



So that AT = ia ■ . r d&. 



cosi — yu,eos r 



