Displacement of Fringes, Fringes, Interference of Fringes, Interference of Light

Displacement of Fringes, Fringes, Interference of Fringes, Interference of Light

DISPLACEMENT OF FRINGES

If a thin glass or mica strip or any other transparent plate of uniform thickness is introduced in the path of one of the two interfering beam from two coherent sources then central bright fringe will be displaced. This displacement from C to C00 will towards the side of lamina.

In order to calculate the displace we shall find the path difference between two beam from coherent sources S1 and S2 at any point ‘P’ on the screen. Let ‘t’ be the thickness of sheet and ‘μ’ the refractive index of its materials.

Time T taken by the beam to reach from S1 to P is given by

where C is the velocity in air and V is velocity of light in the medium of the plate

The condition for maxima

If P is the centre of the nth bright fringe

Shift of Central Fringe

Shift of central bright fringe where n=0 is given by

This expression is independent of n. This indicate that all the bright fringes are displaced through the same amount equal to  similarly it can be shown that the displacement of any dark fringe is also

The fringe width ω is given by