Estimate the distance (in cm) between the central bright region and the third dark fringe on a screen 5.00 m from two double slits 0.500 mm apart illuminated by 500-nm light.

y = 1.75 cm

Explanation:

In the double-slit experiment the equation for destructive interference is

           d sin tea = (m + ½)

λ

let's use trigonometry to find the angle

         tan θ = y / L

as all the experiment does not occur at small angles

          tan θ = sin θ / cos θ = sin θ = y / L

we substitute

        y = (m + 1/2 ) λ  L / d

we calculate

         y = (3 + ½) 500 10⁻⁹ 5.00 / 0.5 10⁻³

         y = 1.75 10⁻² m

         y = 1.75 cm

1 - wave length

2 - amplitude

3 - crest

4 - trough

explanation:

duh.