Question

2. A pair of narrow, parallel slits sep by 0.25 mm is illuminated by 546 nm green light. The interference pattern is observed on a screen situated at 1.3 m away from the slits. Calculate the distance from the central maximum to the

Answer 1

for the first interference m = 1 y = 2,839 10-3 m

for the second interference m = 2 y = 5,678 10-3 m

Step-by-step explanation:

The double slit interference phenomenon, for constructive interference is described by the expression

d sin θ = m λ

where d is the separation between the slits, λ the wavelength and m an integer that corresponds to the interference we see.

In these experiments in general the observation screen is L >> d, let's use trigonometry to find the angles

tan θ = y / L

with the angle it is small,

tan θ = sin θ / cos θ = sin θ

we substitute

sin θ = y / L

d y / L = m λ

the distance between the central maximum and an interference line is

y = m λ L / d

let's reduce the magnitudes to the SI system

λ = 546 nm = 546 10⁻⁹ m

d = 0.25 mm = 0.25 10⁻³ m

let's substitute the values

y = m 546 10⁻⁹ 1.3 / 0.25 10⁻³

y = m 2,839 10⁻³

the explicit value for a line depends on the value of the integer m, for example

for the first interference m = 1

the distance from the central maximum to the first line is y = 2,839 10-3 m

for the second interference m = 2

the distance from the central maximum to the second line is y = 5,678 10-3 m