Coherent light with wavelength 603 nm passes through two very narrow slits, and the interference pattern is observed on a screen a distance of 3.00 m from the slits. The first-order bright fringe is a distance of 4.84 mm from the center of the central bright fringe. Required:
For what wavelength of light will the first-order dark fringe (the first dark fringe next to a central maximum) be observed at this same point on the screen?

λ  = 4.023 10⁻⁷ m

Explanation:

The double-slit interference phenomenon is described by

          d sin θ = (m + ½) λ          destructive interference

          d sin θ = m λ                  constructive interference

we can use trigonometry

         tan θ = y / L

how these experiments occur for small angles

         tan θ = sin θ/cos θ = sin θ

         sin θ = y / L

we substitute

        d y / L = (m + ½) λ        destructive interference

        d y / L = m λ                 constructive interference

with the expression for constructive interference we look for the separation of the slits

        d = m λ L / y

        d = 1 603 10⁻⁹ 3 /4.84 10⁻³

        d = 3.738 10⁻⁴ m

Now let's analyze the case where the distance for constructive and destructive interference occurs at the same point y = 4.84 mm = 4.84 10⁻³m

          d y / L = (m + ½)  λ

          λ =

the first strip is for m = 1  

let's calculate

         λ  =

         λ  = 4.023 10⁻⁷ m

report!

explanation:

physics means: "the branch of science concerned with the nature and properties of matter and energy. the subject matter of physics, distinguished from that of chemistry and biology, includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms."