460 Prof, Miller on the appearance of a Luminous Pointy 8fc. 



between limits corresponding to the boundary of A P QD, 



=/pQsin{2^{.<-B+f.)}, 



from .r = K E to .r = K R. 



VQ=e . Let-74-=w,-— (w^-B +4KE)= <b. 



y \ A b 



Then the wave transmitted through an aperture A B D would 

 cause at M a displacement 



= / — (KF-a;)sin {4> + 2?«(a;- K E)}, 

 from x = KEtoa;=KF, 



1 — cos 2 m Y . { \ sin 2 w y 



— 2 '- sm ($ + ^ I — ■— 



) 



cos <^. 



In like manner the wave transmitted through an aperture 

 A C D would cause at M a displacement 



1 — cos 2 7n 8 . 

 = e : — 3-7=; — - snid) 



■^'iYTn- 



sin 2 w /3 



] cos 4). 



4^ m^ ^ ""' "^ ' " V 2 ;» 4 m^ /3 



Hence, observing that 2 S = ^ «, the wave transmitted 

 through the aperture ABC will produce at M a displace- 

 ment 



~ ^2m^u^y '\f (l-cos2my)-y(I-cos2m^)J^sin4j 



S 



2 ni" 



—rT- -l B s\n2 m y — y sin*Zm ^K cos <p. 

 u^y\ J 



The intensity of the light at M is expressed by the sum of 

 the squares of the coefficients of sin (p and cos <p. 



{/S(l-cos 2 my) — y (1— cos2w/3)}2 

 + {;Q sin 2 w y — y sin 2 m ^}^ 



= 4 {/8 (sin m yY —- y (sin m ^Y]'^ 



+ 4 {/Ssinwycoswy— ysin?«^cosw/3]2 A 



= 4 y8^ (sin m yf + 4 y^ (sin m ^f 

 — 8^y sin w yS sin m y cos w a, 

 since y = a + /3. 



In the above expression any two of the quantities a, ^^ y, 

 may be interchanged without altering its value. Hence, the 

 intensity of the light at M will be expressed by 



K E G R 



H F 



