In a diffraction study, a narrow slit of width 0.12mm is illuminated by an unknown monochromatic source. Rather than placing a screen, the experimenter mounts a photodiode on a rotating arm that measures the angular position of intensity minima relative to the original beam direction. The first dark band is found at an angle of 0.26∘. The second dark band is not measured.
(a) Determine the wavelength of the light using the measured angle of the first dark band. Do not assume a small‐angle approximation.
(b) If a screen were instead placed 1.50m from the slit, calculate the linear distance on the screen between the central maximum and the first dark band.
(c) Using the result from part (b), compute the percent error that would arise if the small‐angle approximation were used to convert the linear distance into an angle before evaluating the wavelength.