niKOKY AM) TECH.MQIES 



Constructive Interference 

 (Phase difference: zero) 



Wave 



Destructive Interference 

 (Phase difference half wavelength) 



Wave 



Wave 2 



Resultant 



General Interference 



Wave I 



Wove 2 



Resultant 

 (zero) 



"\ T 



\ / 



N Resultant 



Fig. 1. Examples of interference of two waves of equal amplitude. In constructive interference, 

 where the waves are in phase, the amplitudes add at each point. The resultant amplitude is twice the 

 original, as shown on the third line. In destructive interference, the phase difference is one-half wave- 

 length, and the algebraic sum of the two waves is zero at each point. In the general case, where the 

 phase difference is neither zero nor a half -wavelength the resultant can also be obtained by adding al- 

 gebraically the amplitudes of the two waves at each point. 



is a plane perpendicular to the direction of 

 propagation, over which the phase is every- 

 where the same. For a wave diverging from 

 a point source or converging toward a point 

 image the surface of constant phase is spheri- 

 cal. 



The optical path between two points is 

 the product of the physical distance and the 

 index of refraction of the medium. If there 

 are several different media along the light 

 path the total optical path is the sum of the 

 optical paths through each medium, meas- 

 ured along the path followed by the ray. 

 In interferometry, where two beams are 

 separated and later recombined, the optical 

 path difference, or OPD, is just the difference 

 in total optical paths encountered by the two 

 beams while they were separated. 



Several types of interference microscopes 

 use polarized light but in a manner somewhat 

 different than in the polarizing microscope. 

 In the latter, one beam of plane polarized 



light is incident on the specimen. On enter- 

 ing a birefringent specimen, plane polarized 

 light is broken into two components, which 

 are in phase with each other as they enter 

 the specimen (Figs. 2a and 2b). If the optic 

 axis of the specimen lies in the plane perpen- 

 dicular to the original direction of the light 

 one of the beams consists of vibration paral- 

 lel to, the other perpendicular to, the optic 

 axis of the specimen. These two beams travel 

 through the birefringent specimen at differ- 

 ent velocities, so that they emerge out of 

 phase (2a). In general their resultant is no 

 longer plane polarized light, but it is ellip- 

 tically polarized (1). This light cannot be 

 extinguished by an analyzer. Therefore in 

 the polarizing microscope, such a specimen 

 appears bright in the field. 



In interference microscopes which utilize 

 polarized light, relatively thick plates of bi- 

 refringent material are used to separate 

 physically the two beams, as shown in Fig. 



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