Light is sent through a single slit of width w = 0.68 mm. On a screen, which is L = 1.1 m from the slit, the width of the central maximum is D = 4.58 mm. Part A) The angle of the first dark fringe is θdark. Express sin(θdark) in terms of the wavelength of the light λand w. Part (b) Express tan(θdark) in terms of D and L. Part (c) If D << L, how is tan(θdark) related to sin(θdark)? Part (d) Express λ in terms of w, D, and L. Part (e) Solve for the numerical value of λ, in nanometers.

Light is sent through a single slit of width w = 0.68 mm. On a screen, which is L = 1.1 m from the slit, the width of the central maximum is D = 4.58 mm. Part A) The angle of the first dark fringe is θdark. Express sin(θdark) in terms of the wavelength of the light λand w. Part (b) Express tan(θdark) in terms of D and L. Part (c) If D << L, how is tan(θdark) related to sin(θdark)? Part (d) Express λ in terms of w, D, and L. Part (e) Solve for the numerical value of λ, in nanometers.

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