ACHROMATIC DIFFRACTION PLATE 95 



sumed that the object specimen is non-absorbing and has an optical 

 path greater than that of its surround, unless otherwise specified. 



If a dark-contrast diffraction plate is to be achromatized for a wave- 

 length Xi at the blue end of the spectrum and for a wavelength X2 at the 

 red end of the spectrum, the following two equations must be satisfied: 



m - ria = - — ; (2.8) 



ng - n4 = - — • (2.9) 



In Eqs. 2.8 and 2.9, 



m = refractive index of conjugate area for Xi; 

 n^ = refractive index of conjugate area for X2; 

 n2 = refractive index of complementary area for Xi ; . 

 ^4 = refractive index of complementary area for X2; 

 t = thickness of the conjugate and the complementary area. 



The refractive index of dielectrics is greater for the shorter wavelengths 

 of the visible range than for the longer wavelengths. Therefore, let 



% = «i -ch] (2.10) 



?U = n2 — (h. (2.11) 



If Eqs. 2.10 and 2.11 are substituted into Eqs. 2.8 and 2.9 and if it is 

 eliminated from these equations, then 



{d2 -di) ^ b^ll ^n, - na). (2.12) 



Xi 



Equation 2.12 also follows if a bright-contrast diffraction plate is achro- 

 matized at Xi and X2. However, to produce dark contrast it must be 

 true that (ni — n2) < 0; therefore, according to Eq. 2.12 the dis- 

 persion of the material forming the conjugate area must be greater than 

 the dispersion of the material forming the complementary area. To 

 produce bright contrast it must be true that (ni — ^2) > 0, and in this 

 case Eq. 2.12 states that the dispersion of the material forming the com- 

 plementary area must be greater than the dispersion of the material 

 forming the conjugate area. The same two dielectric substances may be 

 used in making either an achromatic dark-contrast or an achromatic 

 bright-contrast diffraction plate provided that each one of these sub- 

 stances is applied over the correct area of the diffraction plate. The 

 material with the higher refractive index must have the lower dispersion. 

 When Eq. 2.12 is satisfied, the diffraction plate is achromatized at Xi and 



