Interference Phenomena. 537 



distribution of energy in the spectrum is correct. The dif- 

 ference between the ordinates of B and the curve C may be 

 taken to measure the amount of interference. The curve D 

 gives the assumed distribution of energy in the grating- 

 spectrum, the abscissae being wave-lengths drawn to such a 

 scale that a particular value of the wave-length is placed at 

 that point of the screen at which the corresponding homo- 

 geneous radiation would have its first principal maximum. 

 Analytically the curves are represented (jj and z being the 

 ordinates and abscissae) by the equations 



y=2-r2 e -* 2 (4rZ± + 3-12z 2 ), . . . . (C) 



y=l*e-«*l* (D) 



Assuming the illumination due to the one source alone to 

 be E , the principal features of the curve (J are : — 



(1) At the intersection of the screen and mirror the illu- 

 mination is 4E . 



(2) The intensity diminishes until a value of z is reached 



for which 2 = -| — v / J = '275 (or £ = *524). The total energy 

 is then 2E , and at this point we may say that no interference 

 takes place. 



(3) The intensity diminishes still further, and now becomes 

 less than that due to the sum of the two separate sources. The 

 minimum intensity takes place when 



s 2 =f- </§ =0-919 (0=0-959). 



The value of E at this point becomes 0*78 E , or only about 

 three quarters of the energy due to each source alone. 



(4) The intensity increases again, and at a point for which 



2 2 =j4- V|| = 2*725 (0 = 1*65) it is once more equal to 2E . 



(5) A maximum of intensity takes place when 



z 2 = %+ V§ = 4*081 (0=2*02). 



The maximum is not very pronounced, its value being 2*24 E . 



(6) The intensity diminishes and gradually approaches the 

 value 2E . The total excess of energy on the screen vanishes 

 as 



J. 



6-* 2 (40 4 + 3-120V0 = O. 







As a result of our calculation, we may say that in all cases 

 where interference is produced by an artificial doubling of 

 the source, such as in Fresnel's mirrors or biprisms, or in 

 Lloyd's mirror-arrangement, the true interference-curve with 



