When a glass plate of refractive index 1.44 is introduced in the path of one of the interfering beams, the fringes are displaced by a distance ' y '. If this plate is replaced by another plate of same thickness but of refractive index 1.66 , the fringes will be displaced by a distance

Step-by-step solution

The displacement of fringes due to the introduction of a glass plate of thickness t and refractive index is given by y = D d ( - 1)t For the first plate with refractive index ₁ = 1.44 , the displacement is y = D d (1.44 - 1)t = 0.44 D d t For the second plate with refractive index ₂ = 1.66 and the same thickness t , the new displacement y' is y' = D d (1.66 - 1)t = 0.66 D d t Taking the ratio of the two displacements, we get y' y = 0.66 0.44 = 3 2 y' = 3y 2 Answer: 3y 2