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).
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.