To find the wavelength of light in this scenario, we can use the double-slit interference equation:
d * sin(θ) = n * λ,
where d is the slit separation, θ is the angle of the bright fringe from the center line, n is the order of the bright fringe, and λ is the wavelength of light.
In this case, we are given: d = 0.060 mm = 0.060 x 10^(-3) m, θ = the angle whose tangent is (9 cm / 2.4 m) = 0.09 m / 2.4 m, n = 4.
First, we need to find the value of θ:
θ = atan(0.09 m / 2.4 m) = 2.2647 degrees.
Now we can rearrange the equation to solve for the wavelength:
λ = (d * sin(θ)) / n.
Substituting the given values:
λ = (0.060 x 10^(-3) m * sin(2.2647 degrees)) / 4.
Using trigonometric functions in radians, we need to convert the angle to radians:
θ_radians = 2.2647 degrees * (π / 180 degrees) = 0.0395 radians.
Now we can calculate the wavelength:
λ = (0.060 x 10^(-3) m * sin(0.0395 radians)) / 4.
Using a scientific calculator:
λ ≈ 4.23 x 10^(-7) m.
Therefore, the approximate wavelength of light in this scenario is 4.23 x 10^(-7) meters.