Can you please clarfiy each answer step by step and why please? A single slit of

Question

Can you please clarfiy each answer step by step and why please?

A single slit of width 2.20 times 10^-6 m is illuminated by a white beam and produces a diffraction pattern on a screen that is 2.30 m away. The whole system in air/vacuum. Is the central fringe on the screen a dark fringe or a bright fringe? If it's a bright fringe, what is its color? Find the diffraction angle (in degrees) of the first dark fringe for the light of wavelength 511 nm in the beam. Find the linear distance on the screen from the center of the diffraction pattern to the first dark fringe for the light of wavelength 511 nm in the beam. What is the width of the central fringe for the light of wavelength 511 nm. If the Whole system is now immersed in water, would the central fringe become wider or the above result in air/vacuum? Why?

Explanation / Answer

central fringe will be white as no dispersion of differenct colors occured

slit width * sin(theta) = order * wavelength

2.2 * 10^-6 * sin(theta) = 1 * 511 * 10^-9

theta = 13.43 degree

linear distance = distance from the screen * tan(theta)

linear distance = 2.3 * tan(13.43)

linear distance = 0.549210 m

fringe width = 2 * order * wavelength * screen distance / slit width

fringe width = 2 * 1 * 511 * 10^-9 * 2.3 / (2.2 * 10^-6)

fringe wifth = 1.068 m

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