Split Lens Modification Homework Help, Assignment Help, Online Tutor, Tutoring

Submit Assignment

* *

Payment Online Assignment Help

Thermodynamics

Homework Help

sfsf

Split Lens Modification

Meslin modified the Billet split lens to produced circular fringes. The two portions of the Billet split lens L₁ and L₂ are made coplanar and the lower portion L₂ is displaced through a distance y. A monochromatic source S is used and light passing through L₁forms an image of the source at A and that passing through L₂ forms an image of the source at B. The two sources A and B are coherent and the fringes are produced on a screen normal to A and B. The screen is situated between A and B.

Consider any point P in the interference field. The light reaching P from S through L₁ transverses an optical path d₁ + AP, where d₁ is the optical path from S to A. Moreover, d₁ is constant because S and A are conjugate points. Similarly, light reaching P from S through L₂ transverses an optical path = d₂ – BP, where d₂ is optical path from S to B.

Here d₂ is constant because S and B are conjugate points. Therefore, the path difference between the rays reaching P is given by

x = (d₂ – BP) – (d₁ + AP)

x = (d₂ – d₁) – (BP + AP)

But, d₂ – d₁ is constant.

Therefore, for x to be constant, (BP + AP) should be constant. Thus, the locus of the points for which the optical path difference (x) should be constant, will be an ellipsoid of revolution having A and B as foci. The cross-section of this surface by a plane normal to AB will be a circle. Hence, alternatively bright and dark circular fringes will be formed on the screen. Here, the beams interfere only on one side. Therefore semicircular fringes will be produced on the screen.