Question

Light falls on two slits 0.0000716 m apart and produces an interference pattern in which
the fourth-order fringe is 0.038 m from the central fringe on a screen 1.0 m away.
A) What is the wavelength of the light?
B) Roughly what color is the light?

Answer 1

Answer:

λ = 6.802 10⁻⁷ m,  wavelength corresponds to orange almost red

Explanation:

The expression for constructive interference is

          d sin θ = m λ

let's use trigonometry

          tan θ = y / L

          tan θ = sin θ / cos θ

interference experiments angles are very small

         tan θ = sin  θ = y / L

substituting

          $d \ \frac{y}{L}$ = m λ

in this case they indicate the separation of the slits d = 7.16 10-5 m, the order of the interference is m = 4, the distance y = 3.8 10-2 m and the separation to the screen L = 1 m

A) they ask us for the wavelength

         λ = $\frac{d y}{ m L}$

let's calculate

         λ = 7.16 10⁻⁵  3.8 10⁻² /(4 1)

         λ = 6.802 10⁻⁷ m

B) Let's reduce the wavelength to nm

          λ = 6.802 10⁻⁷ m (109 nm / 1m)

          λ = 680.2 nm

this wavelength corresponds to orange almost red