Question

Blue light (λ = 475 nm) is sent through a single slit with a width of 2.1 µm. What is the maximum possible number of bright fringes, including the central maximum, produced on the screen? (Hint: What is the largest angle that can be used?)

Answer 1

m = 4

Step-by-step explanation:

The expression that explains the constructive interference of a diffraction pattern is

a sin θ = m λ

where a is the width of the slit and λ the wavelength

sin θ = m λ / a

The maximum value is for when the sine is 1, let's substitute

1 = m λ/a

m = a /λ

let's reduce the magnitudes to the SI system

a = 2.1 um = 2.1 10⁻⁶

lam = 475 nm = 475 10⁻⁹ m

let's calculate

m = 2.1 10⁻⁶ / 475 10⁻⁹

m = 4.42

with m must be an integer the highest value is

m = 4