Question

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

Answer 1

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

Step-by-step 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