Question

"If a beam of monochromatic light is passed though a slit of width 15 μm and the second order dark fringe of the diffraction pattern is at an angle of 5.2o from the central axis, what is the wavelength of the light?"

Answer 1

λ= 5.4379 10⁻⁷ m = 543.79 nm

Step-by-step explanation:

The phenomenon of diffraction is described by the expression for destructive diffraction is

a sin θ = (m + 1/2) λ

λ = a sin θ / (m + 1/2)

let's reduce the magnitudes to the SI system

a = 15 um = 15 10⁻⁶ m

m = 2

θ = 5.2º

Let's calculate

λ = 15 10⁻⁶ sin 5.2 / (2 +1/2)

λ = 5.4379 10⁻⁷ m

Let's reduce to nm

λ= 5.4379 10⁻⁷ m = 543.79 nm