Interference (continuation)

Figure 12 show a transparent film of uniform thickness illuminated by monochromatic light of wavelength l from a point source S. The eye is positioned so that a particular incident ray I from the source enters the eye as ray r₁, after reflection from the front surface of the film at a. The incident ray also enters the film at a as a refracted ray and is reflected from the back surface of the film at b; it then emerges from the front surface of the film at c and also enters the eye as ray r₂. The geometry of Fig 12 is such that r₁ and r₂ are parallel. Having originated in the same point source, they are also coherent and so are capable of interfering. Because these two rays have traveled over paths of different lengths, have traversed different media, and have suffered different kinds of reflection at a and b, there is a phase difference between them. The intensity perceived by the eye, as the parallel rays from the region ac of the film enter it, is determined by this phase difference.

For near-normal incidence (q₁» 0 in Fig. 12) the geometrical path difference for the two paths from S is close to 2d. We might expect the resultant wave reflected from the film near a to be an interference maximum if the distance 2d is an integral number of wavelengths. This statement must be modified for two reasons.