Light falls on a double slit with slit separation
of 2.45×10^−6m, and the first bright fringe is seen at an angle of 13.8◦ relative to the central maximum.
What is the wavelength of the light?
To find the wavelength of the light, we can use the double-slit interference equation:
λ = (d * sin(θ)) / m
Where:
- λ is the wavelength of the light
- d is the slit separation
- θ is the angle of the fringe relative to the central maximum
- m is the order of the fringe
In this case, the first bright fringe corresponds to m = 1.
Let's substitute the given values into the equation:
λ = (2.45×10^−6m * sin(13.8◦)) / 1
First, convert the angle from degrees to radians:
θ = 13.8◦ * (π/180) ≈ 0.2409 radians
Now we can calculate the wavelength:
λ = (2.45×10^−6m * sin(0.2409)) / 1
Calculating the right side of the equation:
λ = (2.45×10^−6m * 0.238) / 1
Finally, solving for λ:
λ ≈ 5.825×10^−7 meters or 582.5 nm
Therefore, the wavelength of the light is approximately 5.825×10^−7 meters or 582.5 nm.