In a Young's double slit experiment, the interference pattern on the screen has a ratio of maximum to minimum intensity equal to 25 : 9 . The ratio of the widths of the two slits used in the experiment is

Step-by-step solution

The ratio of maximum to minimum intensity in an interference pattern is given by I_ max I_ min = ( A₁ + A₂ A₁ - A₂ )^2 Given that I_ max I_ min = 25 9 , we have: ( A₁ + A₂ A₁ - A₂ )^2 = 25 9 Taking the square root of both sides: A₁ + A₂ A₁ - A₂ = 5 3 3A₁ + 3A₂ = 5A₁ - 5A₂ 2A₁ = 8A₂ A₁ A₂ = 4 1 The intensity of light from a slit is directly proportional to its width ( w ) and also proportional to the square of its amplitude ( A^2 ). Therefore, the ratio of the slit widths is: w₁ w₂ = I₁ I₂ = ( A₁ A₂ )^2 = ( 4 1 )^2