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A train of plane light waves is incident on a barrier containing two narrow slits separated by a distance ‘d’. The widths of the slits are small compared with wavelength of the light used, so that interference occurs in the region where the light from S1 overlaps that from S2. A series of alternately bright and dark bands can be observed on a screen placed in this region of overlap.

The variation in light intensity along the screen near the centre O shown in the figure

Now consider a point P on the screen. The phase difference between the waves at P

Similarly for destructive interference,

(n = 1, 2, ………)

Fringe Width W

It is the separation of two consecutive maxima or two consecutive minima.

Near the centre O [where  is very small],

W = yn+1 – yn [yn gives the position of nth maxima on screen]

Intensity Variation on Screen.

If A and Io represent amplitude of each wave and the associated intensity on screen, then, the resultant intensity at a point on the screen corresponding to the angular position theta(0)  as in above figure, is given by

Illustration 1: A beam of light consisting of two wavelengths 6500 oA and 5200 oA is used to obtain interference fringes in YDE. The distance between the slits is 2.0 mm and the distance between the plane of the slits and the screen is 120 cm.

(a) Find the distance of the third bright fringe on the screen from the central maxima for the wavelength 6500 oA.

(b) What is the least distance from the central maxima where the bright fringes due to both the wavelengths coincide?

Solution:

Displacement of Fringes

When a film of thickness ‘t’ and refractive index ‘’ is introduced in the path of one of the sources, then fringe shift occurs as the optical path difference changes.

Optical path difference at

Illustration 1: Monochromatic light of wavelength of 600 nm is used in a YDSE. One of the slits is covered by a transparent sheet of thickness 1.8 x 10-5 m made of a material of refractive index 1.6. How many fringes will shift due to the introduction of the sheet?

Solution:

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