Incident light of wavelength =800 ~nm produces a diffraction pattern on a screen 1.5 ~m away when it passes through a single slit of width 0.5 ~mm . The distance between the first dark fringes on either side of the central bright fringe is

Step-by-step solution

The condition for the first dark fringe in a single slit diffraction pattern is given by a = n , where a is the slit width, is the wavelength, and n = 1 for the first dark fringe. Since is very small, = y D , where y is the distance of the fringe from the central maximum and D is the distance to the screen. Substituting the values: a ( y D ) = y = D a . Given = 800 nm = 800 10⁻⁹ m , D = 1.5 m , and a = 0.5 mm = 0.5 10⁻³ m . y = 800 10⁻⁹ 1.5 0.5 10⁻³ = 1200 10⁻⁹ 0.5 10⁻³ = 2400 10⁻⁶ m = 2.4 10⁻³ m = 2.4 mm . The dis