In a Young's double slit experiment set up, the two slits are kept 0.4 mm apart and screen is placed at 1 m from slits. If a thin transparent sheet of thickness 20 ~m is introduced in front of one of the slits then center bright fringe shifts by 20 mm on the screen. The refractive index of transparent sheet is given by 10 , where is _ _ _ _ .

Step-by-step solution

In Young's Double Slit Experiment, when a thin transparent sheet of thickness t and refractive index is introduced in front of one slit, the central bright fringe shifts by a distance y . The formula for the shift is given by y = D d ( - 1)t . Given values: Distance between slits d = 0.4 mm = 0.4 10⁻³ m Distance to screen D = 1 m Thickness of sheet t = 20 m = 20 10⁻⁶ m Shift y = 20 mm = 20 10⁻³ m Substituting the values into the formula: 20 10⁻³ = 1 0.4 10⁻³ ( - 1) 20 10⁻⁶ 20 10⁻³ = 20 10⁻⁶ 0.4 10⁻³ ( - 1) 20 10⁻³