Question

You find an unmarked blue laser on your way to physics class. When you get to class you realize you can determine the wavelength of the laser by doing a double slit experiment. Shining the laser through a double slit with a slit separation of 0.342 mm on the wall 2.12 m away the first bright fringe is 2.80 mm from the center of the pattern. What is the wavelength

Answer 1

Answer:

λ = 451.7 nm

Explanation:

The expression for the constructive interference of the double diffraction experiment is

          d sin θ = m λ

let's use trigonometry

          tan θ = y / L

   

how the experiment occurs at very small angles

          tan θ = sin θ / cos θ = sin θ

          sin θ = y / L

we substitute

         d y / L = m λ  

         λ = $\frac{d \ y}{m \ L}$

let's calculate

          λ = $\frac{0.342 \ 10^{-3} \ 2.80 \ 10^{-3} }{1 \ 2.12 }$

          λ = 4.51699 10⁻⁷ m

          λ = 4.517 10⁻⁷ m (109 nm / 1m)

          λ = 451.7 nm