Two transparent slabs of equal thickness but distinct refractive indices ₁ and ₂ are joined side by side to create a composite slab. This slab is positioned immediately after the double slit in a Young's experiment, ensuring that light from one slit passes through one material and light from the other slit passes through the other material. What must be the minimum thickness of the slab to produce a minimum at the po

Step-by-step solution

Assume the thickness of the slabs is t . The optical path length for light from the first slit to P₀ is S₁P₀ + ( ₁ - 1)t . The optical path length for light from the second slit to P₀ is S₂P₀ + ( ₂ - 1)t . Since P₀ is equidistant from the slits, S₁P₀ = S₂P₀ . The path difference at P₀ is: x = |(S₁P₀ + ( ₁ - 1)t) - (S₂P₀ + ( ₂ - 1)t)| = | ₁ - ₂|t For a minimum intensity at P₀ , the path difference must be an odd multiple of 2 : x = (2n - 1) 2 For the minimum thickness, taking n = 1 gives x = 2 . Equating the path di