# 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

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

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1 year 2021-09-05T02:12:56+00:00 1 Answers 12 views 0

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

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