A laboratory bench is set up so that monochromatic green light of wavelength λ=550nm passes through a narrow vertical slit and strikes a screen located L=2.00m downstream. A camera records the light intensity I across the screen as a function of the horizontal displacement y from the central maximum. The first minimum on either side of the center is found at y=±4.8mm, and the second minimum is at y=±9.6mm. No other information is provided.
(a) Calculate the width of the slit. Express your answer to three significant figures.
(b) Using your result from part (a), predict the distance from the central maximum to the first minimum that would be observed if the same apparatus were illuminated with violet light of wavelength λ=420nm.
(c) Comment on whether the small–angle assumption is justified for the green–light measurement described above. Support your answer numerically.