In Fraunhoffer diffraction pattern width of central bright fringe is β. If wavelength of light is doubled and slit width is halved, distance of second dark fringe from the centre of central bright fringe is

If ‘a’ be the width of the slit and λ be the wavelength of light used. Then β=2λa. In the second case width of central maxima is β1=2λ1a1=22λa2=42λa=4β∴ Width of first secondary maxima =β12=2β∴ Distance of second dark fringe = Half of the width of central bright fringe + width of first secondary bright fringe=β12+β12=β1=4β