A double slit apparatus is fitted with a mica strip and a polystyrene strip on its two slits. The thickness of the strips is 0.50 mm , while the separation between the slits is 0.12 cm . The refractive indices of mica and polystyrene are 1.58 and 1.55 respectively for the light of wavelength 590 nm used in the setup. The interference pattern is observed on a screen positioned one meter away. At what distance from the

Step-by-step solution

The path difference introduced by the two strips at the center of the screen is given by: x₀ = ( ₁ - 1)t - ( ₂ - 1)t = ( ₁ - ₂)t Substituting the given values: x₀ = (1.58 - 1.55) 0.50 10⁻³ = 0.03 0.50 10⁻³ = 1.5 10⁻⁵ m The number of fringes by which the central maximum is shifted is: n₀ = x₀ = 1.5 10⁻⁵ 590 10⁻⁹ = 15000 590 25.42 The path difference at a distance y from the center of the screen is: x = x₀ y d D For a maximum, the path difference must be an integral multiple of the wavelength, x = n . Thus, the posit