In a Young's double slit experiment, the initial angular fringe width is 0.1^ and the corresponding linear fringe width is 2 mm . The experimental setup is modified such that the new angular fringe width becomes 0.15^ and the new linear fringe width becomes 4 mm . The ratio of the new screen distance to the initial screen distance ( D₂ D₁ ) is:

Step-by-step solution

The linear fringe width and the angular fringe width are related by the equation: = D where D is the distance of the screen from the slits. Rearranging for D , we get: D = The ratio of the new screen distance to the initial screen distance is: D₂ D₁ = ( ₂ ₁ ) ( ₁ ₂ ) Substituting the given values: ₁ = 2 mm , ₂ = 4 mm ₁ = 0.1^ , ₂ = 0.15^ D₂ D₁ = ( 4 2 ) ( 0.1 0.15 ) = 2 ( 2 3 ) = 4 3 Answer: 4 3