Question

A parallel beam of light falls on two small slits 5x10-5 m apart.
A) If the distance between the central and 1st fringe is 0.06 m and the light is being
projected onto a screen 5 m away, what is the wavelength of the light?
B) Roughly what color is it?

Answer 1

Answer:

  λ = 6 10⁻⁷ m, color orange

Explanation:

This problem is about the interference phenomenon, constructive interference occurs when the path difference is equal to an integer number of wavelengths

          d sim θ = m λ

Let's use trigonometry, remembering that the angles for these experiments are very small.

          Sin θ = y / L

          tan θ = $\frac{sin \theta}{cos \theta}$ = sin θ

          sin θ = y / L

we substitute

         $d \ \frac{y}{L} = m \lambda$

A) Donut length is requested

        λ = $\frac{d \ y}{m \ L}$

let's calculate

        λ = 5 10⁻⁵ 0.06 /( 1  5)

        λ = 6 10⁻⁷ m

B) let's express the wavelength in nm

      λ = 6 10⁻⁷ m = 600 nm

this corresponds to the color orange