Light shines through a single slit whose width is 5.7 × 10-4 m. A diffraction pattern is formed on a flat screen located 4.0 m away. The distance between the middle of the central bright fringe and the first dark fringe is 3.9 mm. What is the wavelength of the light?
To find the wavelength of light, we can use the formula for the distance between the central bright fringe and the first dark fringe in a single slit diffraction pattern:
y = (λ * L) / w
where:
y is the distance between the central bright fringe and the first dark fringe
λ is the wavelength of the light
L is the distance between the single slit and the screen
w is the width of the single slit
We are given the following values:
y = 3.9 mm = 3.9 × 10^-3 m
L = 4.0 m
w = 5.7 × 10^-4 m
Now, we can rearrange the formula to solve for the wavelength (λ):
λ = (y * w) / L
Substituting the given values into the formula:
λ = (3.9 × 10^-3 m * 5.7 × 10^-4 m) / 4.0 m
Calculating the value:
λ = 7.794 × 10^-7 m
Therefore, the wavelength of the light is approximately 7.794 × 10^-7 meters.