12 Mr. T. K. Ohinmayam on the Flow of 



where p is the radius o£ curvature of the reflected wave on 

 emergence at Q. Since p = a0/2 approximately, 



p aO 



/ o + QP"*2 < ^/ + 3a(9 , 



In any plane in advance of that passing through the edge 

 of the cylinder (y = — d, say), the expression for the intensity 

 of illumination at any point is 



1=1 + 5-2^5 008 0, (1) 



where <$> = 2k6 2 (y + ad) and s = a<9/(3a<9 + 2?/). 



The positions of the maxima and minima of illumination 

 are given by 



dl ds I ., cosdA _ r- . , deb _ /rtN 



s-M 1 ~v?) +v ' Bn *3fr =0 ' • • (2) 



Since d$\d6 = ±k6(y + ad) + 2k0 2 a, and contains the factor 

 27r/\, it will be large, so that the first term in equation (2) 

 is negligible. That equation hence becomes 



sin = 0, 

 or 2e 2 (y + a$) = m\/2, (3) 



while the relation between 6 and x is given by 



X={y + a6)20-a0 2 /2 = 2y6 + 3a0 2 l2. . . (4) 



From (1) and (3) it is seen that the intensities of the 

 successive maxima and minima are respectively proportional 

 to 



Imax.- |l+( 3a 0_^) } , 

 Imin= \}-{^0ZZ2d) \ ' 



The intensity-curve has been plotted out in fig. 2 (a) for 

 the case a=l'5 cm. and d—0'2 cm. It will be seen that 

 in this plane I max . begins nearly with a value (1+1) 2 = 4 

 and drops down gradually in successive fringes to a limiting 

 value of (l + l/v / 3) 2 = 2 , 49 approx. I min . increases from a 

 value nearly zero to a limiting value (1 — 1/\/3) 2 = 0"18 

 approx. The visibility of the successive fringes in the plane 

 of observation therefore decreases slowly. 



At the plane y = 0, the illumination is given by 



I = l + i— 2cos0/\/3. . . ... (5) 



The intensity-curve is shown in fig. 2 (b). I max . has a 



