In a Young's double slit experiment, the ratio of the slit widths is 1:9 . The ratio of the resultant intensity at the central maximum to the resultant intensity at a point on the screen where the path difference is 3 ( being the wavelength of light) is :

Step-by-step solution

The intensity of light passing through a slit is directly proportional to its slit width. Since the ratio of slit widths is 1:9 , the ratio of intensities is I₁ : I₂ = 1:9 . Let I₁ = I and I₂ = 9I . The intensity at the central maximum (where phase difference is zero) is: I_ max = ( I₁ + I₂ )^2 = ( I + 9I )^2 = (I + 3I)^2 = 16I For a point on the screen with a path difference x = 3 , the corresponding phase difference is: = 2 x = 2 ( 3 ) = 2 3 The resultant intensity at this point is: I_P = I₁ + I₂ + 2 I₁ I₂ I_P =