As an admirer of Thomas Young, you perform a double-slit experiment in his honor. You set your slits 1.15 mm apart and position your screen 3.93 m from the slits. Although Young had to struggle to achieve a monochromatic light beam of sufficient intensity, you simply turn on a laser with a wavelength of 647 nm . How far on the screen are the first bright fringe and the second dark fringe from the central bright fringe

a) y = 2.21 10⁻³ m, b)  y = 5.528 10⁻³ m

Explanation:

In the double-slit experiment the interferences occur at the positions

         d sin θ = m λ                    constructive interference

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

let's use trigonometry for the angle

          tan θ = y / L

as in this experiment the angles are very small

          tan θ = sin θ/cos θ = sin θ

          sin θ = y / L

we substitute

         d y / L = m λ                   constructive interference

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

Let's answer the questions

a) first line of constructive interference me = 1

          y = m  λ L / d

          y = 1 647 10⁻⁹ 3.93 /1.15 10⁻³

          y = 2.21 10⁻³ m

b) second dark band m = 2

            y = (m + ½) λ L / d

            y = (2 + ½)  647 10⁻⁹ 3.93 /1.15 10⁻³

            y = 5.528 10⁻³ m

0 = 0.40 / 0 = 0

= 0.20 = 9.80 ⁄2 =?

=0 , = = 0.20 =0.50 0 0.40 ⁄

=0−122 =0−12(9.80 ⁄2)(0.50)2 =1.2