In a double-slit experiment, the slits are illuminated by a monochromatic, coherent light source having a wavelength of 527 nm. An interference pattern is observed on the screen. The distance between the screen and the double-slit is 1.54 m and the distance between the two slits is 0.102 mm. A light wave propogates from each slit to the screen. What is the path length difference between the distance traveled by the waves for the fifth-order maximum (bright fringe) on the screen

  Λ = 5.14 10⁻⁴ m

Explanation:

This is a double slit experiment, which for the case of constructive interference

          d sin θ = m λ

let's use trigonometry

         tan θ = y / L

as the angles are very small

         tan θ = = sin θ

         sin θ = y / L

we substitute

         d y / L = m λ

        y = m λ L / d

we calculate for the interference of order m = 5

         y = 5  527 10⁻⁹  1.54/0.102 10⁻³

         y = 3.978 10⁻² m

Now we can find the difference in length between the two rays, that of the central maximum and this

let's use the Pythagorean theorem

           L’=

           L ’=

           L ’= 1.54051 m

optical path difference

          Λ = L’- L

          Λ = 1.54051 - 1.54

          Λ = 5.14 10⁻⁴ m

answer; (arch); good luck