From Engineering Physics: Fundamentals and Modern Applications


Theory of Interference Fringes

Let S be a narrow slit illuminated by monochromatic light of wavelength ?, and S 1 and S 2 be the two narrow slits separated by a small distance 2 d (as in Figure 5). Let a screen XY be placed at a distance D from the coherent sources S 1 and S 2. Let O be the foot of the perpendicular drawn from C, the mid point of S 1 and S 2 on the screen. Now consider a point P on the screen at a distance x from O at which the condition for bright and dark fringes are to be determined. Draw S 1M and S 2N perpendiculars from S 1 and S 2 on the screen and join S 1P and S 2P. The path difference between the waves reaching at P from S 1 and S 2 is given by

In a right angled triangle S 2NP, we have

Figure 5

Using the binomial theorem and neglecting higher terms, since D >> x or d, we get


Similarly in a right angled triangle S 1MP, we have


? Path difference,


If the sources S 1 and S 2 are in the same phase as the waves reaching at P, the path differences must only be due to path difference, ?

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Topics of Interest

4.11 FRESNEL'S BIPRISM Fresnel produced the interference fringes in the laboratory by deriving two coherent sources S 1 and S 2 from a single monochromatic source S by using the deviation produced by...

4.6 ANALYTICAL TREATMENT OF INTERFERENCE We shall derive an expression for the resultant intensity at any point P of the screen due to the superposition of two waves of light. Let S be a narrow slit...

2.8   DIFFRACTION Consider a screen having a small hole with sharp edges at the periphery and dimensions comparable to the wavelength of light (this may be an aperture, a slit, or a grating) and...

4.8 CONDITION FOR SUSTAINED INTERFERENCE OF LIGHT To obtain well defined interference patterns, the intensity at points corresponding to destructive interference must be zero, while intensity at the...

5.1 OVERVIEW We have seen that the interference phenomenon arises due to two or more coherent beams of light obtained either by wavefront division or by amplitude division or both. In this chapter,...