Form of Fringes in Michelson Interferometer

The form of fringes depends on inclination of M₁ and M₂.Let M₂’ formed by reflection at the semi-silvered surface of G₁ so that AM₂’ equal to the interference fringes may be in regarded to be formed by light reflected from the surfaces of M₁ and M₂’.Thus the arrangement is equivalent to an air film inclosed between the reflecting surfaces M₁ and M₂’.

❶Circular fringes:-

When the two mirror are exactly perpendicular to the film M1M2’ is of uniform thickness and we obtain circular fringes.It can be explained as follows-

In the figure M₁ & M₂’ are the parallel reflecting surfaces.The actual source has been replaced by its virtual images formed by reflection in the partially silvered surfaces S’ forms two virtual images S₁ & S₂ in M₁ & M₂’ respectively.The virtual images are separated by distance 2d if the observer looks into the system at an angle 𝛉.The path difference between thhe two beams will be 2dcos𝛉.The total path difference between two beams is given by

∆= 2dcosө+λ/2

The condition for obtaining brightness-

2dcosө+λ/2=mλ, where m=0,1,2,3,4,…………………………….

❷Localised Fringes:-

When the two mirrors are not exactly perpendicular to each other & therefore the mirrors M₁ and the virtual image M₂’ are not exactly  wedge-shape& the fringes appears to be as shown below.

❸White-light fringes:-

If,in the last case,monochromatic light is replaced by white light and if the thickness of the is small,a few curved and coloured localized fringes are obtained,the fringes of zero thickness being again perfectly achromatic and straight.For large thichness of the film,uniform illumination is obtained.