In a Young's double-slit setup, the widths of the two slits are in the ratio 4 : 1 . The ratio of the intensity at the central maximum to the intensity at a point on the screen where the path difference is 4 (where is the wavelength of light used) is :

Step-by-step solution

The intensity of light from a slit is directly proportional to its width. Therefore, the ratio of the intensities of the two slits is: I₁ I₂ = w₁ w₂ = 4 1 Let I₁ = 4I₀ and I₂ = I₀ . The intensity at the central maximum is given by: I_ = ( I₁ + I₂ )^2 I_ = ( 4I₀ + I₀ )^2 = (2 I₀ + I₀ )^2 = (3 I₀ )^2 = 9I₀ For a point on the screen where the path difference is x = 4 , the corresponding phase difference is: = 2 x = 2 4 = 2 The intensity I_P at this point is given by the general interference formula: I_P = I₁ + I₂ + 2