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?

Answer 1

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.