To solve this problem, we can use the formula for the fringe separation in a double-slit interference pattern:
Δy = (λL) / d
Where: Δy is the fringe separation (0.550 mm in this case) λ is the wavelength of light (what we're trying to find) L is the distance from the screen to the double slits (1.85 m) d is the separation between the slits (2.06 mm)
We can rearrange the formula to solve for the wavelength:
λ = (Δy * d) / L
Plugging in the given values:
λ = (0.550 mm * 2.06 mm) / 1.85 m
First, we need to convert all the units to be consistent. Let's convert the distance to meters:
L = 1.85 m
Now, let's calculate the wavelength:
λ = (0.550 mm * 2.06 mm) / 1.85 m
λ = (0.0011 m * 0.00206 m) / 1.85 m
λ = 0.000002266 m
The wavelength of the light is approximately 2.266 nm (nanometers).