Red light of wavelength 633 nm from a helium-neon laser passes through a slit 0.330 mm wide. The diffraction pattern is observed on a screen 2.55 m away. Define the width of a bright fringe as the distance between the minima on either side. a. What is the width of the central bright fringe?
b. What is the width of the first bright fringe on either side of the central one?

a)   y_total = 19.916 10⁻⁵ m ,   b)    Δθ = 1.91 10-⁻³ rad

Explanation

This is a diffraction exercise that is described by the expression

          a sin θ = m λ

the first minimum occurs for m = 1

         a sin θ = λ

        sin θ = λ / a

        θ = sin⁻¹ (633 10⁻⁹ / 0.330 10⁻³)

        θ = 1.918 10⁻³ rad

let's use trigonometry

        tan θ = y / x

        y = x tan θ

        y = 2.55 tan (3.936 10-3)

        y = 5.75 10⁻- m

this value is from the central maximum to one extreme of the value,

        y_ total = 2 y

        y_total = 2 (5.75e1)

        y_total = 19.916 10⁻⁵ m

b) For the second point and constructive inference we have m = 2

         sin θl = m λ

         θ = sin⁻¹ (lat / a)

         θ = sin⁻¹ (2 633 10-9 / 0.33010-3) = son-1 (3.836 10-3)

         θ = 3.84 10-3 give

The width of this maximum is

          Δθ = 1.3 10-3

          Δθ = 3.84 10⁻³- 1.918 10⁻³

          Δθ = 1.91 10-⁻³ rad