The wavelength of the light is 550 nm
For a double slit interference pattern with slit spacing, d we have
dsinθ = mλ where d = slit spacing = 0.22 mm = 0.22 × 10⁻³ m, m = number of maximum fringe = 2(from the picture) and λ = wavelength of light.
Thus sinθ = mλ/d
Also, tanθ = L/D where L = distance between central maximum and fringe = 2.0 cm/2 = 1.0 cm = 1 × 10⁻² m and D = distance between slit and screen = 2.0 m
Since θ is small, sinθ ≅ tanθ
So, mλ/d = L/D
Making λ subject of the formula, we have
λ = dL/mD
Substituting the values of the variables into the equation, we have
λ = dL/mD
λ = 0.22 × 10⁻³ m × 1 × 10⁻² m/(2 × 2.0 m)
λ = 0.22 × 10⁻⁵ m²/4.0 m
λ = 0.055 × 10⁻⁵ m
λ = 0.55 × 10⁻⁶ m
λ = 550 × 10⁻⁹ m
λ = 550 nm
So, the wavelength of the light is 550 nm
Learn more about double slit interference here:
https://brainly.com/question/4449144
