Width of Slit?

Question

A beam of green light, wavelength = 544 nm, is incident normally on a single slit of width w. The diffraction pattern is displayed on a screen placed 1 m from the slit.

The distance between the 1st and 2nd minima of this pattern is measured to be 2.4 cm. Calculate the width of the slit

Answer 1

The ref. says that for a small-angle approximation of the relation between wavelength λ, slit width a, order number of the minimum m, distance to minimum y, and distance from slit to screen D,
y = mλD/a thus distance between minima x = λD/a and a = λD/x = 5.44E-7 m * 1 m / 0.024 m = = 2.267E-5 m.
The small-angle approximation is valid because x/D is small.