Consider a monochromatic X-ray beam with a wavelength of 100 pm passing through a Young's double slit. The resulting interference pattern is recorded on a photographic plate located 40 cm from the slit. Determine the required separation between the slits if the successive maxima on the screen are to be separated by a distance of 0.1 mm .

Step-by-step solution

The fringe width in Young's double slit experiment is given by = D d where is the wavelength, D is the distance to the screen, and d is the slit separation. Given: = 100 pm = 100 10⁻¹² m = 10⁻¹⁰ m D = 40 cm = 0.4 m = 0.1 mm = 10⁻⁴ m Rearranging the formula to solve for d : d = D Substituting the values: d = 10⁻¹⁰ 0.4 10⁻⁴ d = 4 10⁻⁷ m