Question

A double-slit arrangement produces interference fringes for sodium (λ = 589 nm) that are 0.2° apart. What is the angular fringe separation if the entire arrangement is immersed in water (n = 1.33)? 

Answer 1

Angular fringe separation in water

[If the double slit apparatus is immersed in a liquid of refractive index n, the optical path difference between S₂P and S₁P of Fig. 12.1 becomes n(S₂P – S₁P) ≈ (nd x/D ≈ (nd) sin θ. In Eqns. (12.5) and (12.6) d is replaced by (nd) so that the fringe width becomes λD (nd) i.e., the fringes are shrunk].