

Please recheck the problem for correctness of numerals and description. Usually, in single slit experiment, problem will not contain the lens of diameter but would contain the width of the slit. Hence, assuming 0.1 mm to be the width of the slit, let us proceed to solve.
a = width of the slit = 0.1 mm = 1 * 10-4 m
λ = wavelength of light = 500 nm = 500 * 10-9 m
D = distance of the screen = 1m
Width of the central fringe = λD / a = 500 * 10-9 * 1 / 1 * 10-4 = 500 * 10-5 = .5 * 10-2 m = 5mm
