Consider the two-slit interference experiment. Electromagnetic radiation passes through the two slits that are a distance of 0.0170 nm apart. A fourth-order bright fringe forms at an angle of 8.0 degrees relative to the incident beam. What is the wavelength of the light?
To find the wavelength of the light, we can use the formula for the path difference between the two slits for constructive interference:
Path difference = n * λ
where n is the order of the bright fringe (in this case 4), λ is the wavelength of the light, and the path difference is given by:
Path difference = d * sinθ
where d is the distance between the two slits (0.0170 nm) and θ is the angle of the bright fringe (8.0 degrees).
Putting these together, we have:
n * λ = d * sinθ
4 * λ = 0.0170 nm * sin(8.0 degrees)
Now, we need to convert the angle to radians:
8.0 degrees * (π/180) = 0.1396 radians
Plugging this into the equation:
4 * λ = 0.0170 nm * sin(0.1396)
4 * λ = 0.0170 * 0.1389
λ = 0.0170 * 0.1389 / 4
λ = 0.000590 nm
Therefore, the wavelength of the light is 0.000590 nm.