In biprism experiment, the 4^ th dark band is formed opposite to one of the slits. The wavelength of light used is (D=distance between source and screen, d= the distance between the slits)

Step-by-step solution

The position of the n^ th dark band from the central maximum is given by y_n = (2n - 1) D 2d . For the 4^ th dark band, n = 4 . y₄ = (2(4) - 1) D 2d = 7 D 2d The point opposite to one of the slits is at a distance of d 2 from the central maximum. Equating the two distances: 7 D 2d = d 2 7 D = d^2 = d^2 7D Answer: d^2 7D