A vessel ABCD of 10 cm width has two small slits S 1 and S 2 sealed with identical glass plates of equal thickness. The distance between the slits is 0 .8 mm . POQ is the line perpendicular to the plane AB and passing through O , the middle point of S 1 and S 2 , A monochromatic light source is kept at S , 40 cm cm below P and 2 m from the vessel, to illuminate the slits as shown in the figure alongside. After a liqu

Step-by-step solution

Given Y 1 = 40 cm, D 1 = 2 m = 200 cm , D 2 = 10 cm tan α = y 1 D 1 = 4 0 2 0 0 = 1 5 ∴ α = tan -1 1 / 5 sin α = 1 2 6 ≈ 1 5 = tan α Initial path difference Δx 1 , = SS 1 − SS 2 = y 1 d D 1 = y 1 d D 1 & geometrical path difference Δ x 2 S 1 R − S 2 R = - y 2 d D 2 For central maxima, total path difference has to be zero. i.e., y 1 d D 1 - y 2 d D 2 = 0 ⇒ y 2 = y 1 D 2 D 1 = 4 0 cm × 1 0 cm 2 0 0 cm = 2 cm Now as central bright fringe is at Q. them the optical path difference is μ - 1 t & for central maxima μ - 1 t