Two lasers, one red and one blue, are directed in turn through the same narrow slit and onto a screen 1.8m away. The red laser has wavelength 650nm, and the perpendicular distance from the central maximum to the first dark band is measured to be 14.4mm. The blue laser has wavelength 450nm.
(a) Show how the measured distance for the red laser can be used to compute the slit width.
(b) Calculate the numerical value of the slit width.
(c) Using the slit width found in part (b), predict the distance from the central maximum to the first dark band when the blue laser is used.
(d) For the blue-laser result, determine the angle corresponding to the first dark band and comment on whether the small-angle approximation remains valid for that wavelength in this setup.