In a certain two slit diffraction experiment, two slits 0.02mm wide are spaced0.2mm between centers.(a) how many fringes appear between the first minima of the single slit envelopeon either side of the central maximum? (b) if the angle between the central maximum and the second fringe to eitherside of the central maximum is 0.17 degrees, what is the wavelength?

a)   m = 10  and    b)  λ  = 3.119 10⁻⁷ m

Explanation:

In the diffraction experiments the maximums appear due to the interference phenomenon modulated by the envelope of the diffraction phenomenon, for which to find the number of lines within the maximum diffraction center we must relate the equations of the two phenomena.

Interference equation      d sin θ = m λ

Diffraction equation         a sin θ = n λ

Where d is the width between slits (d = 0.2 mm), a is the width of each slit (a = 0.02 mm). θ is the angle, λ the wavelength, m and n  are an integer.

Let's find the relationship of these two equations

    d sin θ / a sin θ = m Lam / n Lam

The first maximum diffraction (envelope) occurs for n = 1, let's simplify

    d / a = m

Let's calculate

    m = 0.2 / 0.02

    m = 10

This means that 10 interference lines appear within the first maximum diffraction.

b) let's use the interference equation, remember that the angles must be given in radians

    θ = 0.17 ° (π rad / 180 °) = 2.97 10⁻³ rad

    d sin  θ = m λ

    λ = d sin θ / m

    λ = 0.2 10⁻³ sin (2.97 10⁻³) / 2

    λ  = 3.119 10⁻⁷ m