A thin paper of thickness 0.02 mm with a refractive index of 1.45 is pasted across one of the slits in a Young's double slit experiment. The paper transmits 4/9 of the incident light energy. The wavelength of the light used is 600 nm . Determine how many fringes will cross through the centre if an identical paper piece is subsequently pasted across the other slit as well.

Step-by-step solution

The path difference introduced by a transparent sheet of thickness t and refractive index is given by x = ( - 1)t . The number of fringes shifted due to this path difference is n = x = ( - 1)t . Substituting the given values: n = (1.45 - 1) 0.02 10⁻³ 600 10⁻⁹ n = 0.45 2 10⁻⁵ 6 10⁻⁷ = 9 10⁻⁶ 6 10⁻⁷ = 15 When the first paper is pasted, the central fringe shifts by 15 fringes. When an identical paper is subsequently pasted across the second slit, the new path difference exactly cancels the initial one, bringing the ce