The figure shows the light intensity on a screen behind a double slit. The slit spacing is 0.22 mm and the screen is 2.0 m behind the slits (Figure 1). What is the wavelength of the light?

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

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