Question

In a two-slit setup, each slit is 0.02 mm wide. These apertures are illustrated by plane waves of sodium light (wavelength = 589.6 nm). The resulting fringe pattern consists of 11 narrow fringes that gradually decrease in intensity with distance from the central maximum. Determine the separation between the slits.,

Answer 1

d = 0.22 mm

Step-by-step explanation:

The phenomenon of interference and diffraction is always present, the latter is the envelope that modulates the process, let's write the equation of each

Interference d sin θ = m λ

Diffraction a sin θ = n λ

Where d is the separation between the slits, a is the width of each, n and m are integers

In general, the most intense diffraction order is the first, so we can do n = 1, divide the two equations

d sin θ/ a sin θ = m λ / λ

d / a = m

They give us the number of interference lines (m = 11), the width of each slit (a = 0.02 mm) and the wavelength (λ = 589.6 nm), let's calculate

d = a m

d = 0.02 11

d = 0.22 mm