A plane light wave of wavelength λ is incident on a narrow slit of width b. The disturbance/pattern on the outgoing side of the slit is to be studied on a screen at a large distance and an angle θ to the normal as shown below. By dividing the slit into j narrow strips of width dx, explain why the phase difference of light from the different strips at the screen is given by 2πdx/λ = sin(θ). (ii) Stating any assumptions you make, show that the total electric field at the screen has the following form: E = E0 * ∫ sin(2πx/λ) dx (iii) Thus, show that the intensity at the screen has the following form: I = I0 * (sin(πb/λsin(θ)))^2 (iv) If the wavelength is 700nm and the width of the slit is 2 microns, estimate: a) The width of the maximum in radians b) The angle of the first two minima for positive theta c) Approximate values for the intensities of the first two maxima relative to the height of the maximum