In a Young's double slit experiment, the separation between consecutive dark fringes is 1.0 mm . The screen is situated at a distance of 2.5 m from the slits, while the separation between the slits is 1.0 mm . Determine the wavelength of the light being used for the experiment.

Step-by-step solution

The separation between consecutive dark fringes is the fringe width . The formula for fringe width is given by: = D d Rearranging for wavelength : = d D Given values are: = 1.0 mm = 1.0 10⁻³ m d = 1.0 mm = 1.0 10⁻³ m D = 2.5 m Substituting the values into the formula: = (1.0 10⁻³) (1.0 10⁻³) 2.5 = 10⁻⁶ 2.5 m = 0.4 10⁻⁶ m = 400 10⁻⁹ m = 400 nm