Estimating measurement uncertainties

We want to determine the width "a" of a diffracting slit from the diffraction pattern observed on a screen located at a distance "D" of the split, which is lit by a laser source of wavelength λ (cf. figure 3).

figure 3 : Experimental situation for the measurement of the width "a" of the split
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What is the expression of the illumination I(θ) on the screen for a split that is considered of nearly infinite length in comparison to its width "a" ?

Express the angle θ according to the distance between the split and the screen D and to the width L of the central lobe of diffraction measured on the screen.

Find another expression of θ from the apparent diameter of the central spot of diffraction deduced from I(θ).

Deduce from these two expressions of θ the relation between the split's width a and quantities L, D and λ .

Using the propagation of uncertainties law, express the standard uncertainty u(a).

Calculate a and u(a) assuming the hypothesis that the wavelength λ of the luminous source (λ=633nm) includes no uncertainty .

Calculate the expanded uncertainty U(a) and express the measurement result of width a.